Monotone Recurrence Relations, Their Birkhoff Orbits and Topological Entropy.
TLDR
In this paper, a generalization of the class of monotone twistmaps to maps of S sub 1 x R sub n is proposed, and the existence of Birkhoff orbits is studied, and a criterion for positive topological entropy is given.Abstract:
: A generalization of the class of monotone twistmaps to maps of S sub 1 x R sub n is proposed. The existence of Birkhoff orbits is studied, and a criterion for positive topological entropy is given. These results are then specialized to the case of monotone twist maps. Finally it is shown that there is a large class of symplectic maps to which the foregoing discussion applies. Keywords: Dynamical systems; Theorems.read more
Citations
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Chaos and time-reversal symmetry. Order and chaos in reversible dynamical systems
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References
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Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
TL;DR: In this article, the authors present an agreement between Publications mathematiques de l'I.H.E.S. and les conditions generales d'utilisation (http://www.numdam.org/legal.php).
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Some remarks on Birkhoff and Mather twist map theorems
TL;DR: A recent result of J. Mather [1] about the existence of quasi-periodic orbits for twist maps is derived from an appropriately modified version of G. D. Birkhoff's classical theorem concerning periodic orbits as mentioned in this paper.
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Bifurcations de points fixes elliptiques. II. Orbites périodiques et ensembles de Cantor invariants.
TL;DR: In this paper, a priori estimations lipschitziennes sur les orbites bien ordonnees are presented. But they do not consider the existence of ensembles invariants d'Aubry-Mather.
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More Denjoy minimal sets for area preserving diffeomorphisms
TL;DR: In this paper, it was shown that the space of Denjoy minimal sets of angular rotation number ω and intrinsic rotation number (ω+R)/n (mod. 1) contains a disk of dimensionn−1.
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The periodic orbits of an area preserving twist map
TL;DR: In this paper, the authors studied the oscillation properties of periodic orbits of an area-preserving twist map, inspired by the similarity between the gradient flow of the associated action-function, and a scalar parabolic PDE in one space dimension.