LI-Yorke sensitivity and other concepts of chaos

  title={LI-Yorke sensitivity and other concepts of chaos},
  author={Sergiǐ Kolyada},
  journal={Ukrainian Mathematical Journal},
  • S. Kolyada
  • Published 1 August 2004
  • Mathematics
  • Ukrainian Mathematical Journal
We give a survey of the theory of chaos for topological dynamical systems defined by continuous maps on compact metric spaces. 
Recent development of chaos theory in topological dynamics
We give a summary on the recent development of chaos theory in topological dynamics, focusing on Li–Yorke chaos, Devaney chaos, distributional chaos, positive topological entropy, weakly mixing sets
Are there chaotic maps in the sphere
Relations between distributional and Devaney chaos.
This article gives explicit examples that any of these two implications of chaos in the sense of Li and Yorke do not hold for distributional chaos.
Li-Yorke Chaos in Hybrid Systems on a Time Scale
This is the first time in the literature that chaos is obtained for DETS, using the reduction technique to impulsive differential equations to prove the presence of chaos in dynamic equations on time scales.
Chaos, attractors and the Lorenz conjecture: Noninvertible transitive maps of invariant sets are sensitive
University of Minnesota M.S. dissertation. July 2010. Major: Mathematics. Advisor: Bruce B. Peckham. 1 computer file (PDF); iv, 36 pages, appendices A-C.
Relativization of dynamical properties
In the past twenty years, great achievements have been made by many researchers in the studies of chaotic behavior and local entropy theory of dynamical systems. Most of the results have been
Distributional chaos via semiconjugacy
We develop a new method for proving the existence of distributional chaos. It is based on the special properties of semiconjugacy. As an application we prove that the equation is uniformly
Devaney chaotic fuzzy discrete dynamical systems
  • J. Kupka
  • Computer Science
    International Conference on Fuzzy Systems
  • 2010
Results contained in this contribution are related to the most common definition of chaos, i.e., Devaney's one, and provide almost complete answer to the problem introduced in H. Roma´n-Flores and Y. Chalco-Cano's Chaos, Solitons & Fractals.


Dynamics in One Dimension
Periodic orbits.- Turbulence.- Unstable manifolds and homoclinic points.- Topological dynamics.- Topological dynamics (continued).- Chaotic and non-chaotic maps.- Types of periodic orbits.-
Chaotic Dynamical Systems
The Characteristic Lyapunov Exponents (CLE) are a natural extension of the linear stability analysis to aperiodic motion in dynamical systems. Roughly speaking, they measure the typical rates of the
On li-yorke pairs
The Li–Yorke definition of chaos proved its value for interval maps. In this paper it is considered in the setting of general topological dynamics. We adopt two opposite points of view. On the one
(Communicated by R. Daniel Mauldin)Abstract. We prove, among others, the following relations between notionsof chaos for continuous maps of the interval: (i) A map / is not chaotic inthe sense of Li
A characterization of chaos
Consider the continuous mappings f from a compact real interval to itself. We show that when f has a positive topological entropy (or equivalently, when f has a cycle of order ≠ 2n, n = 0, 1, 2, …)
On the nature of turbulence
A mechanism for the generation of turbulence and related phenomena in dissipative systems is proposed.
Devaney's chaos or 2-scattering implies Li–Yorke's chaos
The basic result of this investigation may be formulated as follows. Consider the set of natural numbers in which the following relationship is introduced: n1 precedes n2 (n1 ≼ n2) if for any
Chaotic functions with zero topological entropy
On caracterise la classe M⊂C°(I,I) des applications chaotiques en ce sens. On montre que M contient certaines appliquations qui ont a la fois une entropie topologique nulle et des attracteurs
Li-Yorke sensitivity
We introduce and study a concept which links the Li–Yorke versions of chaos with the notion of sensitivity to initial conditions. We say that a dynamical system (X,T) is Li–Yorke sensitive if there