Porcupine-like Horseshoes. Topological and Ergodic Aspects
نویسندگان
چکیده
We introduce a class of topologically transitive and partially hyperbolic sets called porcupine-like horseshoes. The dynamics of these sets is a step skew product over a horseshoe. The fiber dynamics is given by a one-dimensional genuinely non-contracting iterated function system. We study this dynamics and explain how the properties of the iterated function system can be translated to topological and ergodic properties of the porcupines.
منابع مشابه
Ergodic Properties of Anosov Maps with Rectangular Holes
We study Anosov diieomorphisms on manifolds in which somèholes' are cut. The points that are mapped into those holes disappear and never return. The holes studied here are rectangles of a Markov partition. Such maps generalize Smale's horseshoes and certain open billiards. The set of nonwandering points of a map of this kind is a Cantor-like set called repeller. We construct invariant and condi...
متن کاملMore on the Shift Dynamics–indecomposable Continua Connection
If X is a compact, locally connected metric space, f : X → X is a homeomorphism, and Q is a closed neighborhood of X, then Z = {p ∈ Q : f(p) ∈ Q for all integers n} is the permanent set for f on Q, and E = {p ∈ Q : there is some positive integer Np such that if n ≥ Np, then f−n(p) ∈ Q} is the entrainment set. In a previous paper, we began a study of the entrainment sets of topological horseshoe...
متن کاملTopological Horseshoe in Travelling Waves of Discretized KdV-Burgers-KS type Equations
Applying the concept of anti-integrable limit to space-time discretized KdV-Burgers-KS type equations, we show that there exist topological horseshoes in the phase space formed by the initial states of travelling wave solutions of the resulted coupled map lattices. In particular, the coupled map lattices display spatio-temporal chaos on the horseshoes.
متن کاملThe Complexity of Permutive Cellular Automata
This paper studies cellular automata in two aspects: Ergodic and topological behavior. For ergodic aspect, the formulae of measure-theoretic entropy, topological entropy and topological pressure are given in closed forms and Parry measure is demonstrated to be an equilibrium measure for some potential function. For topological aspect, an example is examined to show that the exhibition of snap-b...
متن کاملSpecial Session 68: Entropy-Like Quantities and Applications
Entropy is a general concept that appears in different settings with different meanings. Thus, it measures disorder in physics, uncertainty in information theory, minimum code length in coding theory, (pseudo-)randomness in measure-preserving dynamical systems, complexity in topological dynamics, and algorithmic complexity in computer science. As for its importance, let us remind that it enters...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013