Author:
Efremova L. S.,Makhrova E. N.
Abstract
Abstract
The survey is devoted to the topological dynamics of maps defined on one-dimensional continua such as a closed interval, a circle, finite graphs (for instance, finite trees), or dendrites (locally connected continua without subsets homeomorphic to a circle). Connections between the periodic behaviour of trajectories, the existence of a horseshoe and homoclinic trajectories, and the positivity of topological entropy are investigated. Necessary and sufficient conditions for entropy chaos in continuous maps of an interval, a circle, or a finite graph, and sufficient conditions for entropy chaos in continuous maps of dendrites are presented. Reasons for similarities and differences between the properties of maps defined on the continua under consideration are analyzed. Extensions of Sharkovsky’s theorem to certain discontinuous maps of a line or an interval and continuous maps on a plane are considered.
Bibliography: 207 titles.
Reference207 articles.
1. Möbius disjointness conjecture for local dendrite maps;Abdalaoui;Nonlinearity,2019
2. Periodic points and transitivity on dendrites;Acosta;Ergodic Theory Dynam. Systems,2017
3. Topological entropy;Adler;Trans. Amer. Math. Soc.,1965
4. On structurally unstable attracting limit sets of Lorenz attractor type;Afrajmovich;Trans. Moscow Math. Soc.,1982
5. Localized asymptotic solutions of the wave equation with variable velocity on the simplest graphs;Allilueva;Russ. J. Math. Phys.,2017
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献