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September  2009, 25(3): 883-913. doi: 10.3934/dcds.2009.25.883

Hamiltonian dynamics near nontransverse homoclinic orbit to saddle-focus equilibrium

Oksana Koltsova 1, and  Lev Lerman 2,

1. 

Department of Mathematics, Imperial College London, SW7 2AZ, London, United Kingdom
2. 

Research Inst. for Applied Math. and Cybernetics, and Dept. of Diff. Equat., Nizhny Novgorod State University, 603950, Nizhny Novgorod, Russian Federation

Received  October 2008 Revised  April 2009 Published  August 2009

An orbit behavior of a Hamiltonian system in two degrees of freedom in a neighborhood of a quadratically tangent homoclinic orbit to a saddle-focus equilibrium is studied, the orbit structure within the level of the saddle-focus is described. We show the existence of an intrinsic parameter (a modulus) which determines types of invariant nonuniform hyperbolic subsets. These subsets are described by means of symbolic dynamics with countably many states. Multi-round tangent and transversal homoclinic orbits to the saddle-focus have also shown to exist.
Keywords: modulus., saddle-focus, tangent homoclinic orbit, Hamiltonian systems, nonuniformly hyperbolic sets.
Mathematics Subject Classification: Primary: 37D05, 37D25; Secondary: 70H0.
Citation: Oksana Koltsova, Lev Lerman. Hamiltonian dynamics near nontransverse homoclinic orbit to saddle-focus equilibrium. Discrete & Continuous Dynamical Systems, 2009, 25 (3) : 883-913. doi: 10.3934/dcds.2009.25.883
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