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Cantori for symplectic maps near the anti-integrable limit

R S Mackay and J D Meiss

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The authors prove the existence of 'cantori' of all incommensurate rotation vectors, for symplectic maps of arbitrary dimension near enough to any non-degenerate anti-integrable limit, and derive an asymptotic form for them. Cantori are invariant Cantor sets which can be thought of as remnants of KAM tori.


PACS

02.30.Ik Integrable systems

MSC

37J40 Perturbations, normal forms, small divisors, KAM theory, Arnol'd diffusion

37J35 Completely integrable systems, topological structure of phase space, integration methods

37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods

37J10 Symplectic mappings, fixed points

Subjects

Mathematical physics

Dates

Issue 1 (January 1992)



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