COUNTEREXAMPLES IN CHAOTIC GENERALIZED SHIFTS

نویسندگان

چکیده مقاله:

‎In the following text for arbitrary $X$ with at least two elements‎, ‎nonempty countable set $Gamma$‎ ‎we make a comparative study on the collection of generalized shift dynamical systems like $(X^Gamma,sigma_varphi)$ where $varphi:GammatoGamma$ is an arbitrary self-map‎. ‎We pay attention to sub-systems and combinations of generalized shifts with counterexamples regarding Devaney‎, ‎exact Devaney‎, ‎Li-Yorke‎, ‎e-chaoticity and P-chaoticity‎.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

counterexamples in chaotic generalized shifts

‎in the following text for arbitrary $x$ with at least two elements‎, ‎nonempty countable set $gamma$‎ ‎we make a comparative study on the collection of generalized shift dynamical systems like $(x^gamma,sigma_varphi)$ where $varphi:gammatogamma$ is an arbitrary self-map‎. ‎we pay attention to sub-systems and combinations of generalized shifts with counterexamples regarding devaney‎, ‎exact dev...

متن کامل

Chaotic Polynomial Automorphisms; counterexamples to several conjectures

We give a polynomial counterexample to a discrete version of the Markus-Yamabe Conjecture and a conjecture of Deng, Meisters and Zampieri, asserting that if F : C → C is a polynomial map with det(JF ) ∈ C∗, then for all λ ∈ R large enough λF is global analytic linearizable. These counterexamples hold in any dimension ≥ 4.

متن کامل

LI-YORKE CHAOTIC GENERALIZED SHIFT DYNAMICAL SYSTEMS

‎In this text we prove that in generalized shift dynamical system $(X^Gamma,sigma_varphi)$‎ ‎for finite discrete $X$ with at least two elements‎, ‎infinite countable set $Gamma$ and‎ ‎arbitrary map $varphi:GammatoGamma$‎, ‎the following statements are equivalent‎: ‎ - the dynamical system $(X^Gamma,sigma_varphi)$ is‎ Li-Yorke chaotic;‎ - the dynamical system $(X^Gamma,sigma_varphi)$ has‎ an scr...

متن کامل

Generalized Counterexamples to the Seifert Conjecture

Using the theory of plugs and the self-insertion construction due to the second author, we prove that a foliation of any codimension of any manifold can be modified in a real analytic or piecewise-linear fashion so that all minimal sets have codimension 1. In particular, the 3-sphere S has a real analytic dynamical system such that all limit sets are 2-dimensional. We also prove that a 1-dimens...

متن کامل

Examples and Counterexamples of Type I Isometric Shifts

We provide examples of nonseparable spaces X for which C(X) admits an isometric shift of type I, which solves in the negative a problem proposed by Gutek et al. (J. Funct. Anal. 101 (1991), 97-119). We also give two independent methods for obtaining separable examples. The first one allows us in particular to construct examples with infinitely many nonhomeomorphic components in a subset of the ...

متن کامل

Infinite Number of Chaotic Generalized Sub-shifts of Cellular Automaton Rule 180

This paper is devoted to an in-depth study of cellular automaton rule 180 under the framework of symbolic dynamics. Rule 180, a member of Wolfram’s class IV and Chua’s hyper Bernoulli shift rules, defines infinite number of generalized sub-shifts. An effective method of constructing the shift invariant sets of the rule’s global map is proposed. It is noted that this method is also applicable to...

متن کامل

منابع من

با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ذخیره در منابع من قبلا به منابع من ذحیره شده

{@ msg_add @}


عنوان ژورنال

دوره 5  شماره 2

صفحات  85- 97

تاریخ انتشار 2017-02-01

با دنبال کردن یک ژورنال هنگامی که شماره جدید این ژورنال منتشر می شود به شما از طریق ایمیل اطلاع داده می شود.

میزبانی شده توسط پلتفرم ابری doprax.com

copyright © 2015-2023