Invariant circles for the piecewise linear standard map
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In this paper, the authors investigate invariant circles for a one-parameter family of piecewise linear twist homeomorphisms of the annulus and classify them into families, showing that invariant circle of all types and rotation numbers occur.Abstract:
We investigate invariant circles for a one-parameter family of piecewise linear twist homeomorphisms of the annulus. We show that invariant circles of all types and rotation numbers occur and we classify them into families. We compute parameter ranges in which there are no invariant circles.read more
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References
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TL;DR: In this paper, the rotatory motion of a heavy asymmetric rigid body is studied and the theorems of the rotational motion of such a rigid body are formulated and proved.
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Transport in Hamiltonian systems
TL;DR: In this article, the authors developed a theory of transport in Hamiltonian systems in the context of iteration of area-preserving maps, where invariant closed curves present complete barriers to transport, but in regions without such curves there are invariant Cantor sets named cantori, which appear to form partial barriers.
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The discrete Frenkel-Kontorova model and its extensions: I. Exact results for the ground-states
Serge Aubry,P.Y. Le Daeron +1 more
TL;DR: A rigorous study of the ground states of one-dimensional models generalizing the discrete Frenkel-Kontorova model has been presented in this article, where the extremalization equations of the energy of these models turn out to define area preserving twist maps which exhibits periodic, quasi-periodic and chaotic orbits.
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Existence of quasi-periodic orbits for twist homeomorphisms of the annulus
TL;DR: Percival et al. as discussed by the authors defined a set of properties of a pair of nodes, where the nodes correspond to the nodes in a graph and the vertices correspond to nodes in the graph.