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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Christian Bonatti, Lorenzo J. Díaz (2003)
Publications Mathématiques de l'IHÉS
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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.
Marek C. Zdun (1976)
Colloquium Mathematicae
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de Carvalho, André, Hall, Toby (2002)
Experimental Mathematics
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Aleksander Całka (1984)
Colloquium Mathematicae
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Đokovic, Dragomir Z̆., Tingley, Peter W. (2001)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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György Targoński (1977)
Annales Polonici Mathematici
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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.