Nonwandering continuum possessing the Wada property

D. W. Serow

Teoretičeskaâ i matematičeskaâ fizika, Tome 207 (2021) no. 3, pp. 505-520

Résumé

Dynamic systems acting on the plane and possessing the Wada property have been observed. There exist only two topological types, symmetric and antisymmetric, of dissipative dynamic systems with the nonwandering continuum being a common boundary of three regions. An antisymmetric dynamic system with the nonwandering continuum can be transformed into a dynamic system with an invariant vortex street without fixed points. A further factorization procedure allows obtaining a dynamic system having the Wada property with the nonwandering continuum being a common boundary of any finite number of regions. Moreover, following this strategy, it is possible to construct a Birkhoff curve that is a common boundary of two regions (problem $1100$).

Détail

Keywords: dynamic system, Wada basin, Wada property, Birkhoff curve, nonwandering set, rotation number, Schnirelmann density, PostScript.
Mots-clés : indecomposable continuum (atom), composant

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