Forcing relations for homoclinic orbits of the Smale horseshoe map.
Collins, Pieter (2005)
Experimental Mathematics
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Displaying similar documents to “The nonlinearly damped oscillator”
Forcing relations for homoclinic orbits of the Smale horseshoe map.
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Marek C. Zdun (1976)
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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.
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Natural group actions on tensor products of three real vector spaces with finitely many orbits.
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Orbits connecting singular points in the plane
Changming Ding (2005)
Czechoslovak Mathematical Journal
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This paper concerns the global structure of planar systems. It is shown that if a positively bounded system with two singular points has no closed orbits, the set of all bounded solutions is compact and simply connected. Also it is shown that for such a system the existence of connecting orbits is tightly related to the behavior of homoclinic orbits. A necessary and sufficient condition for the existence of connecting orbits is given. The number of connecting orbits is also discussed. ...