Forcing relations for homoclinic orbits of the Smale horseshoe map.
Collins, Pieter (2005)
Experimental Mathematics
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Displaying similar documents to “The forcing relation for horseshoe braid types.”
Forcing relations for homoclinic orbits of the Smale horseshoe map.
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...
The periodic orbit structure of orientation preserving diffeomorphisms on D2 with topological entropy zero
J. M. Gambaudo, S. Van Strien, C. Tresser (1989)
Annales de l'I.H.P. Physique théorique
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Periodic orbits of renormalisation for the correlations of strange nonchaotic attractors.
Mestel, B.D., Osbaldestin, A.H. (2000)
Mathematical Physics Electronic Journal [electronic only]
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On the forcing relation for surface homeomorphisms
Jérôme Los (1997)
Publications Mathématiques de l'IHÉS
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Localization of periodic orbits of autonomous systems based on high-order extremum conditions.
Starkov, Konstantin E. (2004)
Mathematical Problems in Engineering
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How restrictive is topological dynamics?
Anzelm Iwanik (1997)
Commentationes Mathematicae Universitatis Carolinae
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Let be a permutation of an abstract set . In ZFC, we find a necessary and sufficient condition it terms of cardinalities of the -orbits that allows us to topologize 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 -actions without periodic points.