On the orbits of hat-functions
Marek C. Zdun (1976)
Colloquium Mathematicae
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Marek C. Zdun (1976)
Colloquium Mathematicae
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Aleksander Całka (1984)
Colloquium Mathematicae
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György Targoński (1977)
Annales Polonici Mathematici
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Collins, Pieter (2005)
Experimental Mathematics
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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. ...
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...
Zdeněk Sekanina (1968)
Acta Universitatis Carolinae. Mathematica et Physica
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C. Maquera, L. F. Martins (2008)
Annales de la faculté des sciences de Toulouse Mathématiques
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In this paper we describe the orbit structure of -actions of on the solid torus having and as the only compact orbits, and as singular set.