Frequency spanning homoclinic families

Communications in Nonlinear Science and Numerical Simulation

Volumn 8, Issue 3-4, 2003, Pages 149-169

  Rom Kedar, Vered ^a  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

Author keywords

Forced Hamiltonian systems; Homoclinic bifurcations; Turnstile flux

Indexed keywords

BIFURCATION (MATHEMATICS); FUNCTIONS; HAMILTONIANS;

FREQUENCY SPANNING;

NONLINEAR SYSTEMS;

BIFURCATION;

EID: 0042745461     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1007-5704(03)00045-5     Document Type: Article

References (23)

1. Arnold V. Dynamical systems, III, encyclopedia of mathematical sciences 1988 Springer-Verlag Berlin
2. Channon S. Lebowitz J. Numerical experiments in stochasticity and homoclinic oscillations Annals. NY Ac .Sc. 357 1980 108-118
3. Easton R. Trellises formed by stable and unstable manifolds in the plane Trans. Am. Math. Soc. 294 1986 2
4. Elskens Y. Escande D. Slowly pulsating separatrices sweep homoclinic tangles where islands must be small: An extension of classical adiabatic theory Nonlinearity 4 1991 615-667
5. Gelfreich V. Melnikov method and exponentially small splitting of separatrices Physica D 101 3-4 1997 227-248
6. Guckenheimer J. Holmes P. Non-linear oscillations, dynamical systems and bifurcations of vector fields 1983 Springer-Verlag New York, NY
7. Haberman R. Rand R. Yuster T. Resonant capture and separatrix crossing in dual-spin spacecraft Nonlinear Dynam. 18 2 1999 159-184
8. Henrard J. Capture into resonance: An extension of the use of adiabatic invariants Celest. Mech. 27 1982 3-22
9. Kaper T, Wiggins S. Lobe area in adiabatic systems. In: Nonlinear Science: The Next Decade, Proc. CNLS 10th Annual Conf., Physica D
10. Kaper T.J. Kovačič G. A geometric criterion for adiabatic chaos J. Math. Phys 35 3 1994 1202-1218
11. MacKay R. Meiss J. Percival I. Transport in Hamiltonian systems Physica D 13 1984 55-81
12. Meiss J. Symplectic maps, variational principles, and transport Rev. Modern Phys. 64 3 1992 795-848
13. Meiss J. Average exit time for volume preserving maps Chaos 7 1 1997 139-147
14. Neishtadt A. The separation of motions in systems with rapidly rotating phase P.M.M. USSR 48 1984 133-139
15. Neishtadt A.I. Passage through a separatrix in a resonance problem with a slowly-varying parameter Prikl. Mat. Meh. 39 4-6 1975 1331-1334
16. Neshtadt A.I. Chakovski Chernikov A.A. Adiabatic chaos and particle diffusion Sov. Phys. JETP. 72 3 1991 423-430
17. Poincaré H. Les Methods Nouvelles de la Mechanique Celeste 1892 Gauthier-Villars Paris
18. Rom-Kedar V. Poje A.C. Universal properties of chaotic transport in the presence of diffusion Phys. Fluids 11 8 1999 2044-2057
19. Rom-Kedar V. Wiggins S. Transport in two-dimensional maps Arch. Rational Mech. Anal. 109 3 1990 239-298
20. Soto-Trevinõ C. Kaper T.J. Higher-order Melnikov theory for adiabatic systems J. Math. Phys. 37 12 1996 6220-6249
21. Tennyson J.L. Cary J.R. Escande D.F. Change of the adiabatic invariant due to separatrix crossing Phys. Rev. Lett. 56 20 1986 2117-2120
22. Treschev D. Width of stochastic layers in near-integrable two-dimensional symplectic maps Phys. D 116 1-2 1998 21-43
23. Turaev D. Polynomial approximations of symplectic dynamics and richness of chaos in non-hyperbolic area preserving maps. submitted preprint, 2002