Recent development of chaos theory in topological dynamics
arXiv:1503.06425 · doi:10.1007/s10114-015-4574-0
Abstract
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 and so on, and their relationships.
30 pages, Acta Mathematica Sinica, English Series, 2015, published online
References in corpus (4)
Cited by in corpus (22)
- Two results on entropy, chaos, and independence in symbolic dynamics
- Measure-theoretic sensitivity via finite partitions
- Devaney chaos plus shadowing implies distributional chaos
- Mean Li-Yorke chaos along some good sequences
- Finite intersection property and dynamical compactness
- Lyapunov spectrum of separated flows and its dependence on numerical discretization
- Topological disorder triggered by interaction-induced flattening of electron spectra in solids
- Stronger versions of sensitivity for minimal group actions
- Analytical Rayleigh potential for the general relativistic Poynting-Robertson effect
- Positive entropy implies chaos along any infinite sequence
- On dynamics of graph maps with zero topological entropy
- On -tuplewise IP-sensitivity and thick sensitivity
- Chaos for endomorphisms of completely metrizable groups and linear operators on Fréchet spaces
- Pinsker -algebra Character and mean Li-Yorke chaos
- -weakly mixing subsets along a collection of sequences of integers
- Superconvergence of Topological Entropy in the Symbolic Dynamics of Substitution Sequences
- Some properties of circle maps with zero topological entropy
- Directional Pinsker algebra and its applications
- A dynamical version of Kuratowski-Mycielski Theorem and invariant chaotic sets
- Broken family sensitivity in transitive systems
- Dense uniform Li-Yorke chaos for linear operators on a Banach space
- Chaotic sets and Hausdorff dimension for Lüroth expansions