the relation between amplitudes and critical exponents in finite size scaling the relation between critical exponents and the amplitude of the correlation length divergence at the critical point of two dimensional systems as a function of finite size is investigated and generalised in two ways correlations more general than those of order order type are included a form appropriate for anisotropic systems is proposed the authors present a exact results for the ising and gaussian models and b numerical results for the symmetric eight vertex baxter continuous q state potts and continuous n component cubic models

a revision of the lyapunov exponent in 1d quadratic maps abstract only misiurewicz points strictly have a lyapunov exponent positive measure in one dimensional 1d quadratic maps hence we represent here the lyapunov exponent of all the misiurewicz points which were found and inventoried by us in a former work as a result of this representation an infinity of alignments of misiurewicz points are obtained and two types of jumps in the values of are found

pair correlations in the antiperiodic ising strip and conformal invariance an explicit formula for the spatial dependence of the pair correlation function in an ising strip with antiperiodic boundary conditions at the bulk critical temperature is given it follows from the conformal invariance approach of belevin et al 1986 and cardy 1986

finite size scaling in strips antiperiodic boundary conditions the exact values of the universal amplitude a relating the correlation length xi approximately l a to the strip width l at the critical point of ising and 3 state potts models are obtained for the case of antiperiodic or twisted boundary conditions predictions are also made for the finite size scaling behaviour of the interfacial tension

universal scaling law for the largest lyapunov exponent in coupled map lattices coupled map lattices cmls 1 as discrete analogs tocoupled oscillators and partial differential equations havein recent years become the model of choice for developingintuitions and concepts in the study of spatiotemporalchaotic systems among the variety of quantities appliedto characterize the dynamics of a cml the spectrum oflyapunov exponents stands out for its ease of numericalevaluation and for the wealth of information that derivesfrom it for example from pesin s formula 2 thesum of all positive lyapunov exponents provides anestimate of the kolmogorov sinai entropy meanwhile one obtains the information dimension of the chaoticattractor by employing the kaplan yorke conjecture 3 moreover the largest lyapunov exponent lle denotedhenceforth by l quanti es the sensitive dependence oninitial conditions a hallmark of chaos 4 by yieldingthe rate of exponential divergence of two typical nearbytrajectories in this letter we focus on the scaling behavior of lnear certain limiting situations consider a diffusivelycoupled map lattice of the form

conformal invariance and universality in finite size scaling the universal relation between critical exponents and the amplitude of the correlation length divergence as a function of finite size at the critical point of two dimensional systems is shown to be a consequence of conformal invariance both periodic and free boundary conditions are considered

finite size scaling and the two dimensional xy model shows that the finite size scaling assumption and particularly a conjectured relation involving the exponent eta are valid in the low temperature phase of the 2d xy model order by order in a perturbative expansion of the two point correlation function

two dimensional semi infinite multicritical ising models the order parameter correlation functions of the z2 invariant multicritical points in the unitary minimal series of conformal field theory are derived for a semi infinite plane constrained to fixed or free boundary conditions these yield the corresponding universal surface exponents which distinguish the behaviour between even and odd critical models we also make explicit the interplay between duality and boundary conditions

bifurcation diagrams for feedback families of linear systems abstract the purpose of this note is to give a proof of the theorem on the form of bifurcation diagrams for generic feedback families of linear systems announced in 1 the main result stated as theorem 3 1 provides explicit algebraic description of the diagrams

a complete characterization of orbit closures of controllable singular systems under restricted system equivalence in this paper properties of the orbit space of controllable generalized state space systems modulo restricted system equivalence are derived in particular it is shown that this space is a smooth quasiprojective variety of dimension nm then the possible degenerations of controllable systems under transformations of restricted system equivalence are characterized and it is proved that every noncontrollable system can be approximated by a family of controllable systems that belong to a single equivalence class in the single input case this class is uniquely determined whereas in the multivariable case a noncontrollable system may lie in the boundary of finitely or even infinitely many equivalence classes

an analytic estimate of the maximum lyapunov exponent in products of tridiagonal random matrices in this work we present a theoretical and numerical study of the behaviour of the maximum lyapunov exponent in products of random tridiagonal matrices in the limit of small coupling and small fluctuations such a problem is directly motivated by the investigation of coupled map lattices in a regime where the chaotic properties are quite robust and yet a complete understanding has still not been reached we derive some approximate analytic expressions by introducing a suitable continuous time formulation of the evolution equation as a first result we show that the perturbation of the lyapunov exponent due to the coupling depends only on a single scaling parameter which in the case of strictly positive multipliers is the ratio of the coupling strength with the variance of local multipliers an explicit expression for the lyapunov exponent is obtained by mapping the original problem onto a chain of nonlinear langevin equations which are eventually reduced to a single stochastic equation the probability distribution of this dynamical equation provides an excellent description for the behaviour of the lyapunov exponent finally multipliers with random signs are also considered finding that the lyapunov exponent again depends on a single scaling parameter which however has a different expression

scaling behavior of nonhyperbolic coupled map lattices coupled map lattices of nonhyperbolic local maps arise naturally in many physical situations described by discretized reaction diffusion equations or discretized scalar field theories as a prototype for these types of lattice dynamical systems we study diffusively coupled tchebyscheff maps of nth order which exhibit strongest possible chaotic behavior for small coupling constants a we prove that the expectations of arbitrary observables scale with sqrt of a in the low coupling limit contrasting the hyperbolic case which is known to scale with a moreover we prove that there are log periodic oscillations of period ln n2 modulating the sqrt of a dependence of a given expectation value we develop a general 1st order perturbation theory to analytically calculate the invariant one point density show that the density exhibits log periodic oscillations in phase space and obtain excellent agreement with numerical results

a canonical parameterization of the kronecker form of a matrix pencil abstract the kronecker form is the classical canonical form for matrix pencils under strict equivalence transformation consider a matrix pencil whose entries are smooth functions of a parameter vector the kronecker form of the parameterized pencil will in general be a discontinuous function of the parameters for a linear time invariant control system these discontinuities correspond to a change in the finite and infinite invariant zero structure since many control strategies require knowledge of or place restrictions on the zero structure these points of discontinuity are of considerable interest in this paper a general approach to the study of such points is developed in the framework of singularity theory we derive a miniversal parameterization of a given pencil that is a parameterized family of pencils that i includes the given pencil ii is locally equivalent to any other family up to a change of parameters and iii uses the fewest number of parameters to achieve this property all nearby zero structures can be obtained by varying parameter values in the miniversal parameterization from all miniversal parameterizations one having a particularly uncluttered representation is selected as canonical however some restrictions on the finite elementary divisors are then required

duality of ordinary and extraordinary surface critical behaviour in the two dimensional potts model the dual relationship between semi infinite two dimensional q state potts models with free and fixed spin boundary conditions is used to study the surface critical behaviour at the bulk critical temperature with fixed boundary spins i e the extraordinary transition both the magnetisation and energy densities have singularities of the same form mod t tc mod 2 alpha as the bulk free energy at t tc both the spin spin and energy energy correlations decay as r 4 parallel to the surface

dynamic critical behaviour of semi infinite systems conformal invariance and mirror theory the critical dynamics of the d dimensional semi infinite systems is studied at bulk critical temperature as a result of the conformal invariance the dynamic response and correlation functions depend only on the real distance r the image distance r and the time t mirror theory assuming the non conserved order parameter with o n symmetry the authors evaluate the response and correlation functions exactly in the large n limit and also to first order in epsilon 4 d the authors results satisfy the mirror theory for the various types of the phase transitions including the ordinary special anisotropic special and extraordinary transitions

miniversal deformations of linear systems under the full group action abstract we consider the equivalence relation in the space of time invariant linear dynamical systems of the form x ax bu y cx du under the full group action of state feedback output injection transformations as in the case of the reduction of a matrix to its jordan canonical form the reduction of a quadruple a b c d defining a system as above to its canonical reduced form is an unstable operation following v i arnold s techniques the starting point for the study of local perturbations is to obtain a miniversal deformation of a differentiable family of quadruples in this paper a real miniversal deformation and some applications are shown

critical off critical interface in the ising quantum chain and conformal invariance the low energy excitation spectrum of an ising quantum chain in a transverse field which is critical h j 1 for 1 or n or l 2 and off critical h not j for l 2 n or l is calculated up to o l 1 interface critical exponents are determined numerically in the odd sector and exactly in the even sector using finite size scaling one gets an ordinary surface transition when h j and an extraordinary surface transition when h j the gap exponent relation is verified the mass gaps and the level degeneracy are in agreement with conformal invariance

skew symmetric matrix pencils codimension counts and the solution of a pair of matrix equations the homogeneous system of matrix equations x t a ax xb b t bx 0 0 where a b is a pair of skew symmetric matrices of the same size is considered we establish the general solution

conformal invariance and surface defects in the two dimensional ising model exact results the surface critical behavior of the two dimensional ising model with homogeneous perturbations in the surface interactions is studied on the one dimensional quantum version a transfer matrix method leads to an eigenvalue equation for the excitation energies the spectrum at the bulk critical point is obtained using anl 1 expansion wherel is the length of the ising chain it exhibits the towerlike structure which is characteristic of conformal models in the case of irrelevant surface perturbations h s j s 0 as well as for the relevant perturbationh s 0 for which the surface is ordered at the bulk critical point leading to an extraordinary surface transition the exponents are deduced from the gap amplitudes and confirmed by exact finite size scaling calculations both cases are finally related through a duality transformation

solvable model for spatiotemporal chaos we show that the dynamical behavior of a coupled map lattice where the individual maps are bernoulli shift maps can be solved analytically for integer couplings we calculate the invariant density of the system and show that it displays a nontrivial spatial behavior we also introduce and calculate a generalized spatiotemporal correlation function

finite size scaling of the quantum ising chain with periodic free and antiperiodic boundary conditions the authors give exact results for the energy spectrum of a chain of n ising spins in a transverse field with periodic free and antiperiodic boundary conditions the dependence of the energy gaps on boundary conditions is compatible with predictions of conformal invariance for correlation lengths in two dimensional strips the feasibility of calculating surface critical indices using phenomenological renormalisation with free boundary conditions and the convergence for large n are discussed