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Irregular dynamics and homoclinic orbits to Hamiltonian saddle centers

✍ Scribed by Clodoaldo Grotta Ragazzo

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
841 KB
Volume
50
Category
Article
ISSN
0010-3640

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✦ Synopsis

We consider 4-dimensional, real, analytic Hamiltonian systems with a saddle center equilibrium (related to a pair of real and a pair of imaginary eigenvalues) and a homoclinic orbit to it. We find conditions for the existence of transversal homoclinic orbits to periodic orbits of long period in every energy level sufficiently close to the energy level of the saddle center equilibrium. We also consider one-parameter families of reversible, 4-dimensional Hamiltonian systems. We prove that the set of parameter values where the system has homoclinic orbits to a saddle center equilibrium has no isolated points. We also present similar results for systems with heteroclinic orbits to saddle center equilibria.

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