af embeddings into c algebras of real rank zero abstract it is proved that every separable c algebra of real rank zero contains an af sub c algebra such that the inclusion mapping induces an isomorphism of the ideal lattices of the two c algebras and such that every projection in a matrix algebra over the large c algebra is equivalent to a projection in a matrix algebra over the af sub c algebra this result is proved at the level of monoids using that the monoid of murray von neumann equivalence classes of projections in a c algebra of real rank zero has the refinement property as an application of our result we show that given a unital c algebra a of real rank zero and a natural number n then there is a unital homomorphism mn1 mnr a for some natural numbers r n1 nr with nj n for all j if and only if a has no representation of dimension less than n

uniform distribution of eigenfunctions on compact hyperbolic surfaces on demontre que les fonctions propres k du laplacien sur une surface hyperbolique compacte x devient uniformement distribuee sur x quand k

liftings of diagrams of semilattices by diagrams of dimension groups we investigate categorical and amalgamation properties of the functor idc assigning to every partially ordered abelian group g its semilattice of compact ideals idc g our main result is the following theorem 1 every diagram of finite boolean semilattices indexed by a finite dismantlable partially ordered set can be lifted with respect to the idc functor by a diagram of pseudo simplicial vector spaces pseudo simplicial vector spaces are a special kind of finite dimensional partially ordered vector spaces over the rationals with interpolation the methods introduced make it also possible to prove the following ring theoretical result theorem 2 for any countable distributive join semilattices s and t and any field k any v 0 homomorphism f s to t can be lifted with respect to the idc functor on rings by a homomorphism f a to b of k algebras for countably dimensional locally matricial algebras a and b over k we also state a lattice theoretical analogue of theorem 2 with respect to the conc functor and we provide counterexamples to various related statements in particular we prove that the result of theorem 1 cannot be achieved with simplicial vector spaces alone

on the representation of integers by quadratic forms let n 4 and let q 2 z x1 xn be a non singular quadratic form when q is indefinite we provide new upper bounds for the least non trivial integral solution to the equation q 0 and when q is positive definite we provide improved upper bounds for the greatest positive integer k for which the equation q k is insoluble in integers despite being soluble modulo every prime power

diffusion in the standard map abstract diffusion in the standard map is studied numerically the stochasticity parameter k is near the critical value k c and the diffusion coefficient d is calculated it is found to satisfy to a good approximation the scaling relation d k k c with in good agreement with the value predicted by the scaling theory of the disappearance of the last bounding kam torus the critical region where this scaling relation holds is surprisingly large i e k 2 5 the mechanism of transport from the chaotic region to the remnants of the last kam torus is investigated evidence for the existence of a narrow stochastic channel mediating this transport is presented and its origin is discussed although the scaling of d agrees with the predictions of the scaling theory the transport mechanism is different from the one assumed in this theory

spectral spaces of countable abelian lattice ordered groups a compact topological space x is spectral if it is sober i e every irreducible closed set is the closure of a unique singleton and the compact open subsets of x form a basis of the topology of x closed under finite intersections theorem a topological space x is homeomorphic to the spectrum of some countable abelian l group with unit resp mv algebra iff x is spectral has a countable basis of open sets and for any points x and y in the closure of a singleton z either x is in the closure of y or y is in the closure of x we establish this result by proving that a countable distributive lattice d with zero is isomorphic to the lattice of all principal ideals of an abelian l group we say that d is l representable iff for all a b d there are x y d such that a b a y b x and x y 0 on the other hand we construct a non l representable bounded distributive lattice of cardinality 1 with an l representable countable l elementary sublattice in particular there is no characterization of the class of all l representable distributive lattices in arbitrary cardinality by any class of l sentences

markov tree model of transport in area preserving maps abstract transport in an area preserving map with a mixture of regular and chaotic regions is described in terms of the flux through invariant cantor sets called cantori a model retaining a discrete set of cantori approaching a boundary circle gives the markov chain description of hanson cary and meiss the inclusion of cantori surrounding island chains and islands about islands etc gives a markov tree model with a slower decay rate the survival probability distribution is shown to decay asymptotically as a power law the decay exponent agrees reasonably well with the computations of karney and of chirikov and shepelyanski

controllability for a class of area preserving twist maps abstract in this paper we study controllability of two dimensional integrable twist maps with bounded area preserving time dependent control perturbations in contrast to the time independent perturbation case of the kolmogorov arnold moser theorem there are no invariant sets other than the whole phase space if the perturbation is made a function of time we give necessary and sufficient conditions for global controllability of these maps

algebraic decay in self similar markov chains a continuous time markov chain is used to model motion in the neighborhood of a critical invariant circle for a hamiltonian map states in the infinite chain represent successive rational approximants to the frequency of the invariant circle for the case of a noble frequency the chain is self similar and the nonlinear integral equation for the first passage time distribution is solved exactly the asymptotic distribution is a power law times a function periodic in the logarithm of the time for parameters relevant to the critical noble circle the decay proceeds ast 4 05

controlling chaotic dynamical systems abstract we describe a method that converts the motion on a chaotic attractor to a desired attracting time periodic motion by making only small time dependent perturbations of a control parameter the time periodic motion results from the stabilization of one of the infinite number of previously unstable periodic orbits embedded in the attractor the present paper extends that of ott grebogi and yorke phys rev lett 64 1990 1196 allowing for a more general choice of the feedback matrix and implementation to higher dimensional systems the method is illustrated by an application to the control of a periodically impulsively kicked dissipative mechanical system with two degrees of freedom resulting in a four dimensional map the double rotor map a key issue addressed is that of the dependence of the average time to achieve control on the size of the perturbations and on the choice of the feedback matrix

a distributive semilattice not isomorphic to the maximal semilattice quotient of the positive cone of any dimension group abstract we construct a distributive 0 semilattice which is not isomorphic to the maximal semilattice quotient of the positive cone of any dimension group the size of the semilattice is 2

distributive congruence lattices of congruence permutable algebras abstract we prove that every distributive algebraic lattice with at most 1 compact elements is isomorphic to the normal subgroup lattice of some group and to the submodule lattice of some right module the 1 bound is optimal as we find a distributive algebraic lattice d with 2 compact elements that is not isomorphic to the congruence lattice of any algebra with almost permutable congruences hence neither of any group nor of any module thus solving negatively a problem of e t schmidt from 1969 furthermore d may be taken as the congruence lattice of the free bounded lattice on 2 generators in any non distributive lattice variety some of our results are obtained via a functorial approach of the semilattice valued distances used by b jonsson in his proof of whitman s embedding theorem in particular the semilattice of compact elements of d is not the range of any distance satisfying the v condition of type 3 2 on the other hand every distributive 0 semilattice is the range of a distance satisfying the v condition of type 2 this can be done via a functorial construction

quadratic forms and semiclassical eigenfunction hypothesis for flat tori let q x be any integral primitive positive definite quadratic form in k variables where k geq4 and discriminant d for any integer n we give an upper bound on the number of integral solutions of q x n in terms of n k and d as a corollary we prove a conjecture of lester and rudnick on the small scale equidistribution of almost all functions belonging to any orthonormal basis of a given eigenspace of the laplacian on the flat torus mathbb t d for d geq 5 this conjecture is motivated by the work of berry 2 3 on the semiclassical eigenfunction hypothesis

controlling chaotic transport through recurrence abstract transport times for a chaotic system are highly sensitive to initial conditions and parameter values we present a technique to find rough orbits epsilon chains that achieve a desired transport rapidly and which can be stabilized with small parameter perturbations the strategy is to build the epsilon chain from segments of a long orbit the point is that long orbits have recurrences in neighborhoods where faster orbits must also pass the recurrences are used as the switching points between segments the resulting epsilon chain can be refined by gluing orbit segments over the switching points providing that a local hyperbolicity condition is satisfied as an example we show that transport times for the standard map can be reduced by factors of 10 4 the techniques presented here can be easily generalized to higher dimensions and to systems where the dynamics is known only as a time series

controlling hamiltonian chaos the method for stabilizing an unstable periodic orbit in chaotic dynamical systems originally formulated by ott grebogi and yorke ogy is not directly applicable to chaotic hamiltonian systems the reason is that an unstable periodic orbit in such systems often exhibits complex conjugate eigenvalues at one or more of its orbit points in this paper we extend the ogy stabilization method to control hamiltonian chaos by incorporating the notion of stable and unstable directions at each periodic point we also present an algorithm to calculate the stable and unstable directions other issues specific to the control of hamiltonian chaos are also discussed

higher dimensional targeting this paper describes a procedure to steer rapidly successive iterates of an initial condition on a chaotic attractor to a small target region about any prespecified point on the attractor using only small controlling perturbations such a procedure is called targeting previous work on targeting for chaotic attractors has been in the context of one and two dimensional maps here it is shown that targeting can also be done in higher dimensional cases the method is demonstrated with a mechanical system described by a four dimensional mapping whose attractor has two positive lyapunov exponents and a lyapunov dimension of 2 8 the target is reached by making very small successive changes in a single control parameter in one typical case 35 iterates on average are required to reach a target region of diameter 10 sup minus 4 as compared to roughly 10 sup 11 iterates without the use of the targeting procedure

semilattices of finitely generated ideals of exchange rings with finite stable rank we find a distributive v 0 1 semilattice s of size aleph 1 that is not isomorphic to the maximal semilattice quotient of any riesz monoid endowed with an order unit of finite stable rank we thus obtain solutions to various open problems in ring theory and in lattice theory in particular there is no exchange ring thus no von neumann regular ring and no c algebra of real rank zero with finite stable rank whose semilattice of finitely generated idempotent generated two sided ideals is isomorphic to s there is no locally finite modular lattice whose semilattice of finitely generated congruences is isomorphic to s these results are established by constructing an infinitary statement denoted here by urpsr that holds in the maximal semilattice quotient of every riesz monoid endowed with an order unit of finite stable rank but not in the semilattice s

controlling chaos in area preserving maps we describe a method of control of chaos that occurs in area preserving maps this method is based on small modifications of the original map by addition of a small control term we apply this control technique to the standard map and to the tokamap