Area preserving homeomorphisms of open surfaces of genus zero.
Franks, John (1996)
The New York Journal of Mathematics [electronic only]
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Franks, John (1996)
The New York Journal of Mathematics [electronic only]
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Richeson, David, Wiseman, Jim (2003)
The New York Journal of Mathematics [electronic only]
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Franks, John, Handel, Michael (2003)
Geometry & Topology
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W. Ayres (1945)
Fundamenta Mathematicae
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Marc Bonino (2004)
Fundamenta Mathematicae
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We provide a topological proof that each orientation reversing homeomorphism of the 2-sphere which has a point of period k ≥ 3 also has a point of period 2. Moreover if such a k-periodic point can be chosen arbitrarily close to an isolated fixed point o then the same is true for the 2-periodic point. We also strengthen this result by proving that if an orientation reversing homeomorphism h of the sphere has no 2-periodic point then the complement of the fixed point set can be covered...
J. M. Gambaudo, S. Van Strien, C. Tresser (1989)
Annales de l'I.H.P. Physique théorique
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Lluís Alsedà, Vladimir Fedorenko (1993)
Publicacions Matemàtiques
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The continuous self maps of a closed interval of the real line with zero topological entropy can be characterized in terms of the dynamics of the map on its chain recurrent set. In this paper we extend this characterization to continuous self maps of the circle. We show that, for these maps, the chain recurrent set can exhibit a new dynamic behaviour which is specific of the circle maps of degree one.
Lluis Alsedà, Antonio Falcó (1994)
Annales de l'institut Fourier
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We use one-dimensional techniques to characterize the Devil’s staircase route to chaos in a relaxation oscillator of the van der Pol type with periodic forcing term. In particular, by using symbolic dynamics, we give the behaviour for certain range of parameter values of a Cantor set of solutions having a certain rotation set associated to a rational number. Finally, we explain the phenomena observed experimentally in the system by Kennedy, Krieg and Chua (in [10]) related with the appearance...
Jérôme Los (1997)
Publications Mathématiques de l'IHÉS
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Katsuya Yokoi (2007)
Annales Polonici Mathematici
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For a self-map of a compactum we give a necessary and sufficient condition for the chain recurrent set to be precisely the set of periodic points.
Robert F. Williams (1979)
Publications Mathématiques de l'IHÉS
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