Li–Yorke chaos for invertible mappings on compact metric spaces

Abstract

In this paper, we construct a homeomorphism on the unit closed disk to show that an invertible mapping on a compact metric space is Li-Yorke chaotic does not imply its inverse being Li-Yorke chaotic.2000 Mathematics Subject Classification. Primary 37B99, 54H20; Secondary 37C15.

Dynamic Analysis and Cryptographic Application of a Sinusoidal-polynomial Composite Chaotic System

“…Correlation dimension (CD) is applied to illustrate the singularity of attractors in dynamical system [25]. Let S = {s 1 , s 2 , • • • } be a time series and e be embedded dimension, then CD of the S is computed by…”

“…For instance, Wu et al proved that the lattice dynamical system was Li-Yorke chaotic for coupling constant 0 < ε < 1 [34]. Luo et al presented a homeomorphism and showed that an invertible mapping on a compact metric space was Li-Yorke chaotic [25]. Wang et al provided two chaotic systems satisfying Devaney's definition of chaos in [29,30].…”

Reiterative Distributional Chaos on Banach Spaces

“…Exists there chaotic operator, no reiterative distributional chaotic of type 2 on Banach spaces? Before proceeding further, we would like to note that H. Bingzhe and L. Lvlin have shown in [17,Theorem 2.1] that there exists an invertible bounded linear operator T on an infinite-dimensional Hilbert space H such that T is both distributionally chaotic but T −1 is not Li-Yorke chaotic. See also [7,Section 6], where it has been constructed a densely distributionally chaotic operator T ∈ L(l 1 (Z)) such that T is invertible and T −1 is not distributionally chaotic; arguing as in the proof given after Example 2.13 below, we can show that T −1 is densely reiteratively distributionally chaotic of type 1 + and not reiteratively distributionally chaotic of type 2.…”