dynamics of conservative bykov cycles tangencies generalized cocoon bifurcations and elliptic solutions abstract this paper presents a mechanism for the coexistence of hyperbolic and non hyperbolic dynamics arising in a neighbourhood of a conservative bykov cycle where trajectories turn in opposite directions near the two saddle foci we show that within the class of divergence free vector fields that preserve the cycle tangencies of the invariant manifolds of two hyperbolic saddle foci densely occur the global dynamics is persistently dominated by heteroclinic tangencies and by the existence of infinitely many elliptic points coexisting with non uniformly hyperbolic suspended horseshoes a generalized version of the cocoon bifurcations for conservative systems is obtained

applying the hp d version of the fem to locally enhance dimensionally reduced models abstract a modification of the hp d method is presented which allows to locally enhance a dimensionally reduced finite element approximation with an ansatz based on a more accurate i e dimensionally higher model the procedure is based on a hierarchical domain decomposition which is applied to couple discretizations of different types of mechanical models like beams plates and solids thereby the error of the underlying mathematical model can be reduced in critical regions by introducing locally a physically more sophisticated model two examples are given to demonstrate the basic properties of the proposed method in the first example the solution of a one dimensional beam model is improved locally by a two dimensional finite element computation in the second example the local enhancement of a reissner mindlin plate by a fully three dimensional continuum approach is considered yielding a significant reduction of the model error

t points a codimension two heteroclinic bifurcation the local bifurcation structure of a heteroclinic bifurcation which has been observed in the lorenz equations is analyzed the existence of a particular heteroclinic loop at one point in a two dimensional parameter space a t point implies the existence of a line of heteroclinic loops and a logarithmic spiral of homoclinic orbits as well as countably many other topologically more complicatedt points in a small neighborhood in parameter space

abundance of strange attractors in 1976 he h non performed a numerical study of the family of diffeomorphisms of the plane ha b x y 1 ax2 y bx and detected for parameter values a l 4 b 0 3 what seemed to be a non trivial attractor with a highly intricate geometric structure this family has since then been the subject of intense research both numerical and theoretical but its dynamics is still far from being completely understood in particular one could not exclude the possibility that the attractor observed by h6non were just a periodic orbit with a very high period recently in a remarkable paper bc2 benedicks and carleson were able to show that this is not the case at least for a positive lebesgue measure set of parameter values near a 2 b o more precisely they showed that if b 0 is small enough then for a positive measure set of a values near a 2 the corresponding diffeomorphism ha b exhibits a strange attractor their argument is a very creative extension of the techniques they had previously developed in bull for the study of the quadratic family on the real line and no doubt it will be important for the understanding of several other situations of complicated nonhyperbolic dynamics when acquainted in 1985 with the work by benedicks and carleson then in progress palls suggested that one should in this context think of the h6non family as a particular although important model for the creation of a horseshoe and that the emphasis should be put on the occurrence of unfoldings of homoclinic tangencies he proposed that the correct setting for benedicks carleson s results is within this more general framework of homoclinic bifurcations and stated the following

the tric shell element theoretical and numerical investigation the tric facet triangular shell element which is based on the natural mode method is seen under the light of the non consistent formulation proposed by bergan and co workers under this formulation the convergence requirements are fulfilled even with relaxed conditions on the conformity demands of the displacement shape functions the intrinsic connection between the non consistent formulation and the natural mode method is demonstrated establishing thus a rigorous theoretical foundation for the tric element under the perspective of the non consistent formulation tric s convergence characteristics are established by satisfying apriori the patch test due to its inherent properties and thus guaranteeing convergence to the exact solution furthermore the element s accuracy robustness and efficiency are tested in a number of judiciously selected numerical examples on benchmark plate and shell problems while a cpu time comparison with a pure displacement based isoparametric shell element demonstrates its computational merits

uniqueness of connecting orbits in the equation y 3 y2 1 abstract the differential equation of the title arises in particular in the study of shock waves n kopell and l howard advan in math 18 1975 306 358 the equation has two rest points the question is whether there are solutions running between them existence of such connecting solutions is proved independantly in c conley isolated invariant sets and the morse index cont bd math sci no 38 amer math soc providence r i 1978 and kopell and howard ibid the uniqueness is proved in this paper

on the dof region of the mimo gaussian two user interference channel with an instantaneous relay this paper studies inner and outer bounds on the degrees of freedom dof region of the multi antenna two user gaussian interference channel with an instantaneous relay ir or relay without delay it is assumed that the two transmitters and the two receivers have mathop mathrm mathsf m nolimits antennas while the ir receives through mathop mathrm mathsf n r nolimits antennas and transmits through mathop mathrm mathsf n t nolimits antennas in the proposed achievable scheme which generalizes a known one for the case mathop mathrm mathsf m nolimits mathop mathrm mathsf n r nolimits mathop mathrm mathsf n t nolimits to any mathop mathrm mathsf m nolimits mathop mathrm mathsf n r nolimits mathop mathrm mathsf n t nolimits the ir performs memoryless linear operations on its received signal so as to neutralize interference at the receivers and the beamforming matrices used by the ir and the transmitters are jointly designed this joint design strictly outperforms known achievable schemes two outer bounds are derived an information theoretic outer bound is obtained by giving the receivers or the ir genie side information so that the dof region of the resulting enhanced channel is known this converse is valid for any type of processing at the ir and shows the optimality of the proposed achievable scheme for some mathop mathrm mathsf m nolimits mathop mathrm mathsf n r nolimits mathop mathrm mathsf n t nolimits a linear processing outer bound is obtained when the ir is restricted to performs linear operations without any memoryless restriction on its received signal and shows the optimality of the proposed achievable scheme among all linear processing schemes at the ir as a result of independent interest the dof region of the classical multi antenna two user gaussian interference channel without relay when the channel matrices can have any structure is also derived which generalized available dof region results that were derived under certain assumptions on the structure of the channel matrices

dense heteroclinic tangencies near a bykov cycle abstract this article presents a mechanism for the coexistence of hyperbolic and non hyperbolic dynamics arising in a neighbourhood of a bykov cycle where trajectories turn in opposite directions near the two nodes we say that the nodes have different chirality we show that in the set of vector fields defined on a three dimensional manifold there is a class where tangencies of the invariant manifolds of two hyperbolic saddle foci occur densely the class is defined by the presence of the bykov cycle and by a condition on the parameters that determine the linear part of the vector field at the equilibria this has important consequences the global dynamics is persistently dominated by heteroclinic tangencies and by newhouse phenomena coexisting with hyperbolic dynamics arising from transversality the coexistence gives rise to linked suspensions of cantor sets with hyperbolic and non hyperbolic dynamics in contrast with the case where the nodes have the same chirality we illustrate our theory with an explicit example where tangencies arise in the unfolding of a symmetric vector field on the three dimensional sphere

shil nikov configurations in any generic unfolding of the nilpotent singularity of codimension three on r3 abstract we are interested in the dynamics arising in generic unfoldings of the nilpotent singularity of codimension three since shil nikov type homoclinic orbits make up the simplest scenario where very complicated dynamics for three dimensional vector fields can be shown the aim of this paper is to prove analytically their existence in any of such unfoldings

communication over mimo x channels interference alignment decomposition and performance analysis in a multiple antenna system with two transmitters and two receivers a scenario of data communication known as the x channel is studied in which each receiver receives data from both transmitters in this scenario it is assumed that each transmitter is unaware of the other transmitter s data noncooperative scenario this system can be considered as a combination of two broadcast channels from the transmitters points of view and two multiple access channels from the receivers points of view taking advantage of both perspectives two signaling schemes for such a scenario are developed in these schemes some linear filters are employed at the transmitters and at the receivers which decompose the system into either two noninterfering multiple antenna broadcast subchannels or two noninterfering multiple antenna multiple access subchannels the main objective in the design of the filters is to exploit the structure of the channel matrices to achieve the highest multiplexing gain mg it is shown that the proposed noncooperative signaling schemes outperform other known noncooperative schemes in terms of the achievable mg in particular it is shown that in some specific cases the achieved mg is the same as the mg of the system if full cooperation is provided either between the transmitters or between the receivers in the second part of the paper it is shown that by using mixed design schemes rather than decomposition schemes and taking the statistical properties of the interference terms into account the power offset of the system can be improved the power offset represents the horizontal shift in the curve of the sum rate versus the total power in decibels

heteroclinic bifurcations near hopf zero bifurcation in reversible vector fields in r 3 abstract we study the dynamics near a symmetric hopf zero also known as saddle node hopf or fold hopf bifurcation in a reversible vector field in r 3 with involutory an reversing symmetry whose fixed point subspace is one dimensional we focus on the case in which the normal form for this bifurcation displays a degenerate family of heteroclinics between two asymmetric saddle foci we study local perturbations of this degenerate family of heteroclinics within the class of reversible vector fields and establish the generic existence of hyperbolic basic sets horseshoes independent of the eigenvalues of the saddle foci as well as cascades of bifurcations of periodic heteroclinic and homoclinic orbits finally we discuss the application of our results to the michelson system describing stationary states and travelling waves of the kuramoto sivashinsky pde

global bifurcations close to symmetry abstract heteroclinic cycles involving two saddle foci where the saddle foci share both invariant manifolds occur persistently in some symmetric differential equations on the 3 dimensional sphere we analyse the dynamics around this type of cycle in the case when trajectories near the two equilibria turn in the same direction around a 1 dimensional connection the saddle foci have the same chirality when part of the symmetry is broken the 2 dimensional invariant manifolds intersect transversely creating a heteroclinic network of bykov cycles we show that the proximity of symmetry creates heteroclinic tangencies that coexist with hyperbolic dynamics there are n pulse heteroclinic tangencies trajectories that follow the original cycle n times around before they arrive at the other node each n pulse heteroclinic tangency is accumulated by a sequence of n 1 pulse ones this coexists with the suspension of horseshoes defined on an infinite set of disjoint strips where the first return map is hyperbolic we also show how as the system approaches full symmetry the suspended horseshoes are destroyed creating regions with infinitely many attracting periodic solutions

period doubling cascades of attractors a prerequisite for horseshoes this paper shows that if a horseshoe is created in a natural manner as a parameter is varied then the process of creation involves the appearance of attracting periodic orbits of all periods furthermore each of these orbits will period double repeatedly with those periods going to infinity

pq adaptive solid finite elements for three dimensional plates and shells this article presents a pq adaptive finite element procedure for three dimensional computation of thin walled structures like plates and shells the approach is based on a hexahedral element with high order shape functions the polynomial degree of the shape functions in the three spatial directions of the element is adjusted by means of an adaptive procedure to this end a hierarchical error indicator is applied to automatically control the polynomial degree q in thickness and p in the in plane direction of plate and shell like structures the efficiency and reliability of the proposed adaptive method is demonstrated using two numerical examples

asymptotic stability of heteroclinic cycles in systems with symmetry ii systems possessing symmetries often admit robust heteroclinic cycles that persist under perturbations that respect the symmetry in previous work we began a systematic investigation into the asymptotic stability of such cycles in particular we found a sufficient condition for asymptotic stability and we gave algebraic criteria for deciding when this condition is also necessary these criteria are satisfied for cycles in r 3 field and swift and hofbauer considered examples in r 4 for which our sufficient condition for stability is not optimal they obtained necessary and sufficient conditions for asymptotic stability using a transition matrix technique in this paper we combine our previous methods with the transition matrix technique and obtain necessary and sufficient conditions for asymptotic stability for a larger class of heteroclinic cycles in particular we obtain a complete theory for simple heteroclinic cycles in r 4 thereby proving and extending results for homoclinic cycles that were stated without proof by chossat krupa melbourne and scheel a partial classification of simple heteroclinic cycles in r 4 is also given finally our stability results generalize naturally to higher dimensions and many of the higher dimensional examples in the literature are covered by this theory

an achievable rate region for the multiple access channel with feedback an achievable rate region r 1 leq i x 1 y x 2 u r 2 leq i x 2 y x 1 u r 1 r 2 leq i x 1 x 2 y where p u x l x 2 y p u p x l u p x 2 u p y x l x 2 is established for the multiple access channel with feedback time sharing of these achievable rates yields the rate region of this paper this region generally exceeds the achievable rate region without feedback and exceeds the rate point found by gaarder and wolf for the binary erasure multiple access channel with feedback the presence of feedback allows the independent transmitters to understand each other s intended transmissions before the receiver has sufficient information to achieve the desired decoding this allows the transmitters to cooperate in the transmission of information that resolves the residual uncertainty of the receiver at the same time independent information from the transmitters is superimposed on the cooperative correction information the proof involves list codes and block markov encoding

global generic dynamics close to symmetry abstract our object of study is the dynamics that arises in generic perturbations of an asymptotically stable heteroclinic cycle in s 3 the cycle involves two saddle foci of different type and is structurally stable within the class of z 2 z 2 symmetric vector fields the cycle contains a two dimensional connection that persists as a transverse intersection of invariant surfaces under symmetry breaking perturbations gradually breaking the symmetry in a two parameter family we get a wide range of dynamical behaviour an attracting periodic trajectory other heteroclinic trajectories homoclinic orbits n pulses suspended horseshoes and cascades of bifurcations of periodic trajectories near an unstable homoclinic cycle of shilnikov type we also show that generically the coexistence of linked homoclinic orbits at the two saddle foci has codimension 2 and takes place arbitrarily close to the symmetric cycle

spiralling dynamics near heteroclinic networks abstract there are few explicit examples in the literature of vector fields exhibiting complex dynamics that may be proved analytically we construct explicitly a two parameter family of vector fields on the three dimensional sphere s 3 whose flow has a spiralling attractor containing the following two hyperbolic equilibria heteroclinic trajectories connecting them transversely and a non trivial hyperbolic invariant and transitive set the spiralling set unfolds a heteroclinic network between two symmetric saddle foci and contains a sequence of topological horseshoes semiconjugate to full shifts over an alphabet with more and more symbols coexisting with newhouse phenomena the vector field is the restriction to s 3 of a polynomial vector field in r 4 in this article we also identify global bifurcations that induce chaotic dynamics of different types

possible new strange attractors with spiral structure we define a class of three dimensional differential equations which might present strange attractors of a new kind this is illustrated by numerical observations on an explicit example

a new achievable rate region for the interference channel a new achievable rate region for the general interference channel which extends previous results is presented and evaluated the technique used is a generalization of superposition coding to the multivariable case a detailed computation for the gaussian channel case clarifies to what extent the new region improves previous ones the capacity of a class of gaussian interference channels is also established

the p version of the finite element method for three dimensional curved thin walled structures in this paper we present an implementation of a three dimensional p version for structural problems of solids with almost arbitrarily curved surfaces applying the blending function method complex structures can often be modelled by a few p elements being the basis for a higher order approximation numerical examples will demonstrate that the p version with anisotropic ansatz spaces allows to predict the structural behaviour of three dimensional plates and shells with approximately the same amount of degrees of freedom as in the two dimensional case yet significantly more accurate due to the three dimensional model furthermore it is advantageous to compute complex structures exclusively with three dimensional discretizations as no special elements are needed to model the transition from dimensionally reduced formulations like plates or shells to fully three dimensional solid elements using the p version with anisotropic ansatz spaces the whole structure can be efficiently discretized with solid elements even if the aspect ratio of the elements becomes very large copyright 2001 john wiley sons ltd

high order thin walled solid finite elements applied to elastic spring back computations in this paper we present a new approach for computing elastic spring back based on a strictly three dimensional high order solid finite element formulation for curved thin walled structures allowing for an anisotropic discretization in combination with appropriate mesh design the p version yields an exponential rate of convergence in the error in energy norm in contrast to low order elements which yield only an algebraic rate of convergence anisotropic ansatz spaces based on high order elements lead to very efficient discretizations the structural behavior of three dimensional thin walled continua can be predicted with a similar number of degrees of freedom as in the two dimensional case yet significantly more accurately because of the three dimensional model we also introduce an approach for the efficient computation of the relevant geometrically nonlinear problem furthermore the paper describes the necessary model conversion from a low order deep drawing simulation to a spring back computation based on the p version of the fem

estimating the directed information and testing for causality the problem of estimating the directed information rate between two discrete processes x n and y n via the plug in or maximum likelihood estimator is considered when the joint process x n y n is a markov chain of a given memory length the plug in estimator is shown to be asymptotically gaussian and to converge at the optimal rate o 1 sqrt n under appropriate conditions this is the first estimator that has been shown to achieve this rate an important connection is drawn between the problem of estimating the directed information rate and that of performing a hypothesis test for the presence of causal influence between the two processes under fairly general conditions the null hypothesis which corresponds to the absence of causal influence is equivalent to the requirement that the directed information rate be equal to zero in that case a finer result is established showing that the plug in converges at the faster rate o 1 n and that it is asymptotically chi 2 distributed this is proved by showing that this estimator is equal to a scalar multiple of the classical likelihood ratio statistic for the above hypothesis test finally it is noted that these results facilitate the design of an actual likelihood ratio test for the presence or absence of causal influence

capacity results for the discrete memoryless network a discrete memoryless network dmn is a memoryless multiterminal channel with discrete inputs and outputs a sequence of inner bounds to the dmn capacity region is derived by using code trees capacity expressions are given for three classes of dmns 1 a single letter expression for a class with a common output 2 a two letter expression for a binary symmetric broadcast channel bc with partial feedback and 3 a finite letter expression for push to talk dmns the first result is a consequence of a new capacity outer bound for common output dmns the third result demonstrates that the common practice of using a time sharing random variable does not include all time sharing possibilities namely time sharing of channels several techniques for improving the bounds are developed 1 causally conditioned entropy and directed information simplify the inner bounds 2 code trellises serve as simple code trees 3 superposition coding and binning with code trees improves rates numerical computations show that the last technique enlarges the best known rate regions for a multiple access channel mac and a bc both with feedback in addition to the rate bounds a sequence of inner bounds to the dmn reliability function is derived a numerical example for a two way channel illustrates the behavior of the error exponents

channels with block interference a new class of channel models with memory is presented in order to study various kinds of interference phenomena it is shown among other things that when all other parameters are held fixed channel capacity c is an em increasing function of the memory length while the cutoff rate r 0 generally is a em decreasing function calculations with various explicit coding schemes indicate that c is better than r 0 as a performance measure for these channel models as a partial resolution of this c versus r 0 paradox the conjecture is offered that r 0 is more properly a measure of coding delay rather than of coding complexity

a collocated c0 finite element method reduced quadrature perspective cost comparison with standard finite elements and explicit structural dynamics summary we demonstrate the potential of collocation methods for efficient higher order analysis on standard nodal finite element meshes we focus on a collocation method that is variationally consistent and geometrically flexible converges optimally embraces concepts of reduced quadrature and leads to symmetric stiffness and diagonal consistent mass matrices at the same time it minimizes the evaluation cost per quadrature point thus reducing formation and assembly effort significantly with respect to standard galerkin finite element methods we provide a detailed review of all components of the technology in the context of elastodynamics that is weighted residual formulation nodal basis functions on gauss lobatto quadrature points and symmetrization by averaging with the ultra weak formulation we quantify potential gains by comparing the computational efficiency of collocated and standard finite elements in terms of basic operation counts and timings our results show that collocation is significantly less expensive for problems dominated by the formation and assembly effort such as higher order elastostatic analysis furthermore we illustrate the potential of collocation for efficient higher order explicit dynamics throughout this work we advocate a straightforward implementation based on simple modifications of standard finite element codes we also point out the close connection to spectral element methods where many of the key ideas are already established copyright 2014 john wiley sons ltd

reversing symmetries in dynamical systems dynamical systems may possess in addition to symmetries that leave the equations of motion invariant reversing symmetries that invert the equations of motion such dynamical systems are called weakly reversible some consequences of the existence of reversing symmetries for dynamical systems with discrete time mappings are discussed a reversing symmetry group is introduced and it is shown that every weakly reversible mapping l can be decomposed into two mappings k0 and k1 of the same order 2l limit l to infinity included such that k02 k12 i some applications are discussed briefly

chaotic switching in a two person game abstract we study robust long term complex behaviour in the rock scissors paper game with two players played using reinforcement learning the complex behaviour is connected to the existence of a heteroclinic network for the dynamics this network is made of three heteroclinic cycles consisting of nine equilibria and the trajectories connecting them we provide analytical proof both for the existence of chaotic switching near the heteroclinic network and for the relative asymptotic stability of at least one cycle in the network leading to some trajectories paying alternate visits to only two nodes while others follow a complicated sequence of visits to all nodes in the network our results are obtained by making use of the symmetry of the original problem a new approach in the context of learning and they provide an explanation of numerical results previously obtained by other authors

information networks with in block memory a class of channels is introduced for which there is memory inside blocks of a specified length and no memory across the blocks the multiuser model is called an information network with in block memory nibm it is shown that block fading channels channels with state known causally at the encoder and relay networks with delays are nibms a cut set bound is developed for nibms that unifies strengthens and generalizes existing cut bounds for discrete memoryless networks the bound gives new finite letter capacity expressions for several classes of networks including point to point channels and certain multiaccess broadcast and relay channels cardinality bounds on the random coding alphabets are developed that improve on existing bounds for channels with action dependent state available causally at the encoder and for relays without delay finally quantize forward network coding is shown to achieve rates within an additive gap of the new cut set bound for linear additive gaussian noise channels symmetric power constraints and a multicast session

local and global behavior near homoclinic orbits we study the local behavior of systems near homoclinic orbits to stationary points of saddle focus type we explicitly describe how a periodic orbit approaches homoclinicity and with the help of numerical examples discuss how these results relate to global patterns of bifurcations

explosions of chaotic sets abstract large scale invariant sets such as chaotic attractors undergo bifurcations as a parameter is varied these bifurcations include sudden changes in the size and or type of the set an explosion is a bifurcation in which new recurrent points suddenly appear at a non zero distance from any pre existing recurrent points we discuss the following in a generic one parameter family of dissipative invertible maps of the plane there are only four known mechanisms through which an explosion can occur 1 a saddle node bifurcation isolated from other recurrent points 2 a saddle node bifurcation embedded in the set of recurrent points 3 outer homoclinic tangencies and 4 outer heteroclinic tangencies the term outer tangency refers to a particular configuration of the stable and unstable manifolds at tangency in particular we examine different types of tangencies of stable and unstable manifolds from orbits of pre existing invariant sets this leads to a general theory that unites phenomena such as crises basin boundary metamorphoses explosions of chaotic saddles etc we illustrate this theory with numerical examples

causal relay networks in this paper we study causal discrete memoryless relay networks the network consists of multiple nodes each of which can be a source a relay and or a destination in the network there are two types of relays 1 relays with one sample delay strictly causal and 2 relays without delay causal whose transmit signals depend not only on the past received symbols but also on the current received symbols for this network we derive two new cut set bounds one when every node has a message and the other when only the strictly causal relays have messages using the examples of a causal vector gaussian two way relay channel and a causal vector gaussian relay channel we show that the new cut set bounds can be achieved by a simple amplify and forward type relaying our result for the causal relay channel strengthens the previously known capacity result for the same channel by el gamal hassanpour and mammen

precoding for the awgn channel with discrete interference for a state dependent discrete memoryless channel with input alphabet x state alphabet s and output alphabet y where the independent and identically distributed i i d state sequence is known causally at the transmitter it is shown that by using at most min x s s 1 y out of x s inputs of the shannon s derived channel the capacity is achievable as an example of state dependent channels with side information at the transmitter m ary signal transmission for the additive white gaussian noise awgn channel with additive q ary interference where the sequence of i i d interference symbols is known causally at the transmitter is considered the optimal precoding scheme is derived under the constraint that the channel input given any current interference symbol is uniformly distributed over the channel input alphabet it is shown that at low signal to noise ratio snr not doing precoding is optimal for the special case where the gaussian noise power is zero it is shown that the rate log2 m is achievable by a one shot coding scheme if x is an arithmetic progression

normal forms and unfoldings of linear systems in eigenspaces of anti automorphisms of order two abstract in this article we classify normal forms and unfoldings of linear maps in eigenspaces of anti automorphisms of order two our main motivation is provided by applications to linear systems of ordinary differential equations general and hamiltonian which have both time preserving and time reversing symmetries however the theory gives a uniform method to obtain normal forms and unfoldings for a wide variety of linear differential equations with additional structure we give several examples and include a discussion of the phenomenon of orbit splitting as a consequence of orbit splitting we observe passing and splitting of eigenvalues in unfoldings

slepian wolf coding over cooperative relay networks this paper deals with the problem of multicasting a set of discrete memoryless correlated sources dmcs over a cooperative relay network necessary conditions with cut set interpretation are presented a joint source wyner ziv encoding sliding window decoding scheme is proposed in which decoding at each receiver is done with respect to an ordered partition of other nodes for each ordered partition a set of feasibility constraints is derived then utilizing the submodular property of the entropy function and a novel geometrical approach the results of different ordered partitions are consolidated which lead to sufficient conditions for our problem the proposed scheme achieves operational separation between source coding and channel coding it is shown that sufficient conditions are indeed necessary conditions in two special cooperative networks namely aref network and finite field deterministic network also in gaussian cooperative networks it is shown that reliable transmission of all dmcs whose slepian wolf region intersects the cut set bound region within a constant number of bits is feasible in particular all results of the paper are specialized to obtain an achievable rate region for cooperative relay networks which includes relay networks and two way relay networks

time reversal symmetry in dynamical systems a survey abstract in this paper we survey the topic of time reversal symmetry in dynamical systems we begin with a brief discussion of the position of time reversal symmetry in physics after defining time reversal symmetry as it applies to dynamical systems we then introduce a major theme of our survey namely the relation of time reversible dynamical sytems to equivariant and hamiltonian dynamical systems we follow with a survey of the state of the art on the theory of reversible dynamical systems including results on symmetric periodic orbits local bifurcation theory homoclinic orbits and renormalization and scaling some areas of physics and mathematics in which reversible dynamical systems arise are discussed in an appendix we provide an extensive bibliography on the topic of time reversal symmetry in dynamical systems

using lin s method to solve bykov s problems abstract we consider nonwandering dynamics near heteroclinic cycles between two hyperbolic equilibria the constituting heteroclinic connections are assumed to be such that one of them is transverse and isolated such heteroclinic cycles are associated with the termination of a branch of homoclinic solutions and called t points in this context we study codimension two t points and their unfoldings in r n in our consideration we distinguish between cases with real and complex leading eigenvalues of the equilibria in doing so we establish lin s method as a unified approach to re gain and extend results of bykov s seminal studies and related works to a large extent our approach reduces the study to the discussion of intersections of lines and spirals in the plane