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Irregular dynamics and homoclinic orbits to Hamiltonian saddle centers
Author(s) -
Ragazzo Clodoaldo Grotta
Publication year - 1997
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/(sici)1097-0312(199702)50:2<105::aid-cpa1>3.0.co;2-g
Subject(s) - homoclinic orbit , heteroclinic orbit , saddle , hamiltonian system , mathematics , homoclinic bifurcation , hamiltonian (control theory) , eigenvalues and eigenvectors , center (category theory) , mathematical analysis , saddle point , mathematical physics , equilibrium point , periodic orbits , classical mechanics , physics , bifurcation , geometry , quantum mechanics , differential equation , mathematical optimization , chemistry , nonlinear system , crystallography
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. © 1997 John Wiley & Sons, Inc.