LI-Yorke sensitivity and other concepts of chaos

We give a survey of the theory of chaos for topological dynamical systems defined by continuous maps on compact metric spaces.

[1]  A. N. Sharkovskiĭ.  COEXISTENCE OF CYCLES OF A CONTINUOUS MAP OF THE LINE INTO ITSELF , 1995 .

[2]  Jaroslav Smítal,et al.  Chaotic functions with zero topological entropy , 1986 .

[3]  Paul R. Halmos,et al.  Review: W. H. Gottschalk and G. A. Hedlund, Topological dynamics , 1955 .

[4]  Jaroslav Smítal,et al.  CHARACTERIZATIONS OF WEAKLY CHAOTIC MAPS OF THE INTERVAL , 1990 .

[5]  J. Auslander,et al.  Minimal flows and their extensions , 1988 .

[6]  Jonathan L. King,et al.  A map with topological minimal self-joinings in the sense of del Junco , 1990, Ergodic Theory and Dynamical Systems.

[7]  B. Weiss,et al.  Sensitive dependence on initial conditions , 1993 .

[8]  François Blanchard,et al.  On Li-Yorke pairs , 2002, Journal für die reine und angewandte Mathematik (Crelles Journal).

[9]  F. Blanchard,et al.  Asymptotic pairs in positive-entropy systems , 2002, Ergodic Theory and Dynamical Systems.

[10]  B. Weiss,et al.  LOCALLY EQUICONTINUOUS DYNAMICAL SYSTEMS , 2000 .

[11]  F. Takens,et al.  On the nature of turbulence , 1971 .

[12]  V. V. Fedorenko,et al.  Dynamics of One-Dimensional Maps , 1997 .

[13]  Ethan Akin,et al.  When is a Transitive Map Chaotic , 1996 .

[14]  Dynamical systems disjoint from any minimal system , 2004 .

[15]  А. Н. Шарковскуй.  О циклах и структуре непрерынвного отображения , 1965 .

[16]  W. A. Coppel,et al.  Dynamics in One Dimension , 1992 .

[17]  Independent sets of transitive points , 1989 .

[18]  J. Yorke,et al.  Period Three Implies Chaos , 1975 .

[19]  S. Glasner,et al.  Rigidity in topological dynamics , 1989, Ergodic Theory and Dynamical Systems.

[20]  Noninvertible minimal maps , 2001 .

[21]  Harry Furstenberg,et al.  Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation , 1967, Mathematical systems theory.

[22]  R. Ellis.  A semigroup associated with a transformation group , 1960 .

[23]  J. Banks,et al.  Regular periodic decompositions for topologically transitive maps , 1997, Ergodic Theory and Dynamical Systems.

[24]  Wen Huang,et al.  Devaney's chaos or 2-scattering implies Li–Yorke's chaos , 2002 .

[25]  On scrambled sets for chaotic functions , 1987 .

[26]  E. Akin,et al.  Residual properties and almost equicontinuity , 2001 .

[27]  James A. Yorke,et al.  INTERVAL MAPS, FACTORS OF MAPS, AND CHAOS , 1980 .

[28]  Angelo Vulpiani,et al.  Chaotic Dynamical Systems , 1993 .

[29]  L. Snoha,et al.  Stroboscopical property in topological dynamics , 2003 .

[30]  Ethan Akin,et al.  The general topology of dynamical systems , 1993 .

[31]  Jan Mycielski,et al.  Independent sets in topological algebras , 1964 .

[32]  Benjamin Weiss,et al.  Topological transitivity and ergodic measures , 1971, Mathematical systems theory.

[33]  Ethan Akin,et al.  Li-Yorke sensitivity , 2003 .

[34]  K. Sigmund,et al.  Ergodic Theory on Compact Spaces , 1976 .

[35]  A characterization of chaos , 1986, Bulletin of the Australian Mathematical Society.

[36]  M. Misiurewicz,et al.  Combinatorial Dynamics and Entropy in Dimension One , 2000 .

[37]  W. D. Melo,et al.  ONE-DIMENSIONAL DYNAMICS , 2013 .