Strictly ergodic Toeplitz flows with positive entropies and trivial centralizers
A class of strictly ergodic Toeplitz flows with positive entropies and trivial topological centralizers is presented.
Strictly ergodic, uniform positive entropy models
Striped structures of stable and unstable sets of expansive homeomorphisms and a theorem of K. Kuratowski on independent sets
We investigate striped structures of stable and unstable sets of expansive homeomorphisms and continuum-wise expansive homeomorphisms. The following theorem is proved: if f : X → X is an expansive homeomorphism of a compact metric space X with dim X > 0, then the decompositions and of X into stable and unstable sets of f respectively are uncountable, and moreover there is σ (= s or u) and ϱ > 0 such that there is a Cantor set C in X with the property that for each x ∈ C, contains a nondegenerate...
Structure of certain closed flows
Subcontinua of inverse limit spaces of unimodal maps
We discuss the inverse limit spaces of unimodal interval maps as topological spaces. Based on the combinatorial properties of the unimodal maps, properties of the subcontinua of the inverse limit spaces are studied. Among other results, we give combinatorial conditions for an inverse limit space to have only arc+ray subcontinua as proper (non-trivial) subcontinua. Also, maps are constructed whose inverse limit spaces have the inverse limit spaces of a prescribed set of periodic unimodal maps as...
Subshifts of Finite Type and Sofic Systems.
Suites à termes dans un alphabet fini
Sur la construction de mesures selles
Nous construisons des mesures selles (dans un sens faible) pour les endomorphismes holomorphes de .
Sur la répartition des orbites de certains systèmes dynamiques .
Sur les solutions globales de l'équation des cocycles.
Sur les solutions globales de l'équation des cocycles. (Summary).
Sur les trajectoires compactes de systèmes dynamiques autonomes
Systèmes dynamiques topologiques I. Étude des limites de cobords
The Abel equation and total solvability of linear functional equations
We investigate the solvability in continuous functions of the Abel equation φ(Fx) - φ(x) = 1 where F is a given continuous mapping of a topological space X. This property depends on the dynamics generated by F. The solvability of all linear equations P(x)ψ(Fx) + Q(x)ψ(x) = γ(x) follows from solvability of the Abel equation in case F is a homeomorphism. If F is noninvertible but X is locally compact then such a total solvability is determined by the same property of the cohomological equation φ(Fx)...
The Banach contraction mapping principle and cohomology.
The Banach contraction mapping principle and cohomology
By a dynamical system we mean the action of the semigroup on a metrizable topological space induced by a continuous selfmap . Let denote the set of all compatible metrics on the space . Our main objective is to show that a selfmap of a compact space is a Banach contraction relative to some if and only if there exists some which, regarded as a -cocycle of the system , is a coboundary.
The behaviour of the nonwandering set of a piecewise monotonic interval map under small perturbations
In this paper piecewise monotonic maps are considered. Let be a finite union of open intervals, and consider the set of all points whose orbits omit . The influence of small perturbations of the endpoints of the intervals in on the dynamical system is investigated. The decomposition of the nonwandering set into maximal topologically transitive subsets behaves very unstably. Nonetheless, it is shown that a maximal topologically transitive subset cannot be completely destroyed by arbitrary...
The Box Dimension of Completely Invariant Subsets for Expanding Piecewise Monotonic Transformations.
The branch locus for one-dimensional Pisot tiling spaces
If φ is a Pisot substitution of degree d, then the inflation and substitution homeomorphism Φ on the tiling space factors via geometric realization onto a d-dimensional solenoid. Under this realization, the collection of Φ-periodic asymptotic tilings corresponds to a finite set that projects onto the branch locus in a d-torus. We prove that if two such tiling spaces are homeomorphic, then the resulting branch loci are the same up to the action of certain affine maps on the torus.
The centralizer of Morse shifts induced by arbitrary blocks