Author： Haller George Uzer T Palacián Jesús Yanguas Patricia Jaffé Charles
Publisher： IOP Publishing
ISSN： 0951-7715
Source： Nonlinearity, Vol.24, Iss.2, 2011-02, pp. : 527-561
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Abstract
We present a detailed analysis of invariant phase space structures near higher-rank saddles of Hamiltonian systems. Using the theory of pseudo-hyperbolic invariant surfaces, we show the existence of codimension-one normally hyperbolic invariant manifolds that govern transport near the higher-rank saddle points. Such saddles occur in a number of problems in celestial mechanics, chemical reactions, and atomic physics. As an example, we consider the problem of double ionization of helium in an external electric field, a basis of many modern ionization experiments. In this example, we illustrate our main results on the geometry and transport properties near a rank-two saddle.
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