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Hamiltonian dynamics near nontransverse homoclinic orbit to saddle-focus equilibrium

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  • 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.
    Mathematics Subject Classification: Primary: 37D05, 37D25; Secondary: 70H07.


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