Forcing relations for homoclinic orbits of the Smale horseshoe map.
Collins, Pieter (2005)
Experimental Mathematics
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Collins, Pieter (2005)
Experimental Mathematics
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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.
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...
J. M. Gambaudo, S. Van Strien, C. Tresser (1989)
Annales de l'I.H.P. Physique théorique
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Mestel, B.D., Osbaldestin, A.H. (2000)
Mathematical Physics Electronic Journal [electronic only]
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Jérôme Los (1997)
Publications Mathématiques de l'IHÉS
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Starkov, Konstantin E. (2004)
Mathematical Problems in Engineering
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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.