Displaying similar documents to “Periodic orbits and chain-transitive sets of C1-diffeomorphisms”

How restrictive is topological dynamics?

Anzelm Iwanik (1997)

Commentationes Mathematicae Universitatis Carolinae

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Let T be a permutation of an abstract set X . In ZFC, we find a necessary and sufficient condition it terms of cardinalities of the T -orbits that allows us to topologize ( X , T ) as a topological dynamical system on a compact Hausdorff space. This extends an early result of H. de Vries concerning compact metric dynamical systems. An analogous result is obtained for 𝐙 2 -actions without periodic points.

Periodic billiard orbits in right triangles

Serge Troubetzkoy (2005)

Annales de l’institut Fourier

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There is an open set of right triangles such that for each irrational triangle in this set (i) periodic billiards orbits are dense in the phase space, (ii) there is a unique nonsingular perpendicular billiard orbit which is not periodic, and (iii) the perpendicular periodic orbits fill the corresponding invariant surface.