Displaying similar documents to “Orbit Structure of certain ℝ 2 -actions on solid torus”

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 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...

Reidemeister orbit sets

Boju Jiang, Seoung Ho Lee, Moo Ha Woo (2004)

Fundamenta Mathematicae

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The Reidemeister orbit set plays a crucial role in the Nielsen type theory of periodic orbits, much as the Reidemeister set does in Nielsen fixed point theory. Extending Ferrario's work on Reidemeister sets, we obtain algebraic results such as addition formulae for Reidemeister orbit sets. Similar formulae for Nielsen type essential orbit numbers are also proved for fibre preserving maps.