Letelier PS, Motter AE. Homoclinic crossing in open systems: chaos in periodically perturbed monopole plus quadrupolelike potentials.
PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999;
60:3920-7. [PMID:
11970227 DOI:
10.1103/physreve.60.3920]
[Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/1999] [Indexed: 11/07/2022]
Abstract
The Melnikov method is applied to periodically perturbed open systems modeled by an inverse-square-law attraction center plus a quadrupolelike term. A compactification approach that regularizes periodic orbits at infinity is introduced. The (modified) Smale-Birkhoff homoclinic theorem is used to study transversal homoclinic intersections. A larger class of open systems with degenerated (nonhyperbolic) unstable periodic orbits after regularization is also briefly considered.
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