Displaying similar documents to “The forcing relation for horseshoe braid types.”

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.

Periodic orbits and chain-transitive sets of C1-diffeomorphisms

Sylvain Crovisier (2006)

Publications Mathématiques de l'IHÉS

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We prove that the chain-transitive sets of C-generic diffeomorphisms are approximated in the Hausdorff topology by periodic orbits. This implies that the homoclinic classes are dense among the chain-recurrence classes. This result is a consequence of a global connecting lemma, which allows to build by a C-perturbation an orbit connecting several prescribed points. One deduces a weak shadowing property satisfied by C-generic diffeomorphisms: any pseudo-orbit is approximated in the Hausdorff...

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.