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Article

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Accepted version

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2009-04-16

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/193918

Resonant zones, inner and outer splittings in generic and low order resonances of area preserving maps

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https://doi.org/10.1088/0951-7715/22/5/012

Abstract

We consider a one-parameter family of area preserving maps in a neighbourhood of an elliptic fixed point. As the parameter evolves hyperbolic and elliptic periodic orbits of different periods are created. The exceptional resonances of order less than 5 have to be considered separately. The invariant manifolds of the hyperbolic periodic points bound islands containing the elliptic periodic points. Generically, these manifolds split. It turns out that the inner and outer splittings are different under suitable conditions. We provide accurate formulae describing the splittings of these manifolds as a function of the parameter and the relative values of these magnitudes as a function of geometric properties. The numerical agreement is illustrated using mainly the Hénon map as an example.

Subject

Sistemes dinàmics de baixa dimensió, Teoria ergòdica, Homeomorfismes, Difeomorfismes

Subject (English)

Low-dimensional dynamical systems, Ergodic theory, Homeomorphisms, Diffeomorphisms

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

SIMÓ, Carles and VIEIRO YANES, Arturo. Resonant zones, inner and outer splittings in generic and low order resonances of area preserving maps. Nonlinearity. 2009. Vol. 22, num. 5, pags. 1191-1245. ISSN 0951-7715. [consulted: 8 of August of 2026]. Available at: https://hdl.handle.net/2445/193918

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