ha o - dy n / 99 10 00 3 v 1 3 O ct 1 99 9 Chaotic Properties of Subshifts Generated by a Non - Periodic Recurrent Orbit July 1999 Xin -
نویسندگان
چکیده
The chaotic properties of some subshift maps are investigated. These subshifts are the orbit closures of certain non-periodic recurrent points of a shift map. We first provide a review of basic concepts for dynamics of continuous maps in metric spaces. These concepts include nonwandering point, recurrent point, eventually periodic point, scrambled set, sensitive dependence on initial conditions, Robinson chaos, and topological entropy. Next we review the notion of shift maps and subshifts. Then we show that the one-sided subshifts generated by a non-periodic recurrent point are chaotic in the sense of Robinson. Moreover, we show that such a subshift has an infinite scrambled set if it has a periodic point. Finally, we give some examples and discuss the topological entropy of these subshifts, and present two open problems on the dynamics of subshifts.
منابع مشابه
ar X iv : c ha o - dy n / 99 10 00 5 v 1 6 O ct 1 99 9 The Finite - Difference Analysis and Time Flow
متن کامل
ar X iv : c ha o - dy n / 96 06 01 6 v 1 1 J ul 1 99 6 Hopf ’ s last hope : spatiotemporal chaos in terms of unstable recurrent patterns
Spatiotemporally chaotic dynamics of a Kuramoto-Sivashinsky system is described by means of an infinite hierarchy of its unstable spatiotemporally periodic solutions. An intrinsic parametrization of the corresponding invariant set serves as accurate guide to the high-dimensional dynamics, and the periodic orbit theory yields several global averages characterizing the chaotic dynamics.
متن کاملha o - dy n / 99 10 02 0 v 1 1 4 O ct 1 99 9 A Stochastic Approach to the Construction of One - Dimensional Chaotic Maps with Prescribed Statistical Properties
We use a recently found parametrization of the solutions of the inverse Frobenius-Perron problem within the class of complete unimodal maps to develop a Monte-Carlo approach for the construction of one-dimensional chaotic dynamical laws with given statistical properties, i.e. invariant density and autocorrelation function. A variety of different examples are presented to demonstrate the power o...
متن کاملha o - dy n / 99 03 03 2 v 1 2 3 M ar 1 99 9 On the classical dynamics of billiards on the sphere
We study the classical motion in bidimensional polygonal billiards on the sphere. In particular we investigate the dynamics in tiling and generic rational and irrational equilateral triangles. Unlike the plane or the negative curvature cases we obtain a complex but regular dynamics.
متن کاملha o - dy n / 99 10 00 2 v 1 3 O ct 1 99 9 Escape Probability and Mean Residence Time in Random Flows with Unsteady Drift ∗
We investigate fluid transport in random velocity fields with unsteady drift. First, we propose to quantify fluid transport between flow regimes of different characteristic motion, by escape probability and mean residence time. We then develop numerical algorithms to solve for escape probability and mean residence time, which are described by backward Fokker-Planck type partial differential equ...
متن کامل