Chaotic sets of continuous and discontinuous maps

DOI10.1016/j.na.2009.06.075zbMath1181.37041OpenAlexW2076035956MaRDI QIDQ1049520

Changpin Li, Zhan-He Chen, Zeng-Rong Liu, Xin-Chu Fu, Hong-Jun Gao

Publication date: 12 January 2010

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2009.06.075

zbMATH Keywords

chaosshiftscrambled setcontinuous mappiecewise isometrydiscontinuous map

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Symbolic dynamics (37B10) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Chaotic sets of shift and weighted shift maps
• Continuous maps with the whole space being a scrambled set
• Symbolic analysis for some planar piecewise linear maps
• Dynamics of piecewise isometries
• Symbolic representations of iterated maps
• Omega-chaos almost everywhere
• On the geometry of orientation-preserving planar piecewise isometries
• Almost periodicity, chain recurrence and chaos
• Tangents-free property in invariant disk packings generated by some general planar piecewise isometries
• Homeomorphisms with the whole compacta being scrambled sets
• Dynamics of non-ergodic piecewise affine maps of the torus
• Piecewise isometries have zero topological entropy
• ω-Chaos and Topological Entropy
• Riddling and invariance for discontinuous maps preserving Lebesgue measure
• Asymptotic pairs in positive-entropy systems
• Fractal pattern of second-order non-linear digital filters: A new symbolic analysis
• A Chaotic Function with Some Extremal Properties
• Chaos and fractals from third-order digital filters
• A Chaotic Function with a Scrambled Set of Positive Lebesgue Measure
• Continuous chaotic functions of an interval have generically small scrambled sets
• Chaotic Functions with Zero Topological Entropy
• On Scrambled Sets for Chaotic Functions
• On the stability of chaotic functions
• Chaotic Solutions of Systems of First Order Partial Differential Equations
• Scrambled sets of continuous maps of 1-dimensional polyhedra
• Measures of Chaos and a Spectral Decomposition of Dynamical Systems on the Interval
• COMPLEX BEHAVIOR IN DIGITAL FILTERS
• Symbolic dynamics and Markov partitions
• On scrambled sets and a theorem of Kuratowski on independent sets
• Tangencies in invariant disc packings for certain planar piecewise isometries are rare
• On Li-Yorke pairs
• PROPERTIES OF THE INVARIANT DISK PACKING IN A MODEL BANDPASS SIGMA–DELTA MODULATOR
• Criteria for a general continuous self-map to have chaotic sets
• A characterization of chaotic functions with entropy zero via their maximal scrambled sets
• Sofic subshifts and piecewise isometric systems
• Topological size of scrambled sets
• CHAOTIC PROPERTIES OF SUBSHIFTS GENERATED BY A NONPERIODIC RECURRENT ORBIT
• Topological transitivity and ergodic measures
• Hamiltonian mappings and circle packing phase spaces
• Devaney's chaos or 2-scattering implies Li-Yorke's chaos

This page was built for publication: Chaotic sets of continuous and discontinuous maps