Phase change between separatrix crossings in slow-fast Hamiltonian systems

Nonlinearity

Volumn 18, Issue 3, 2005, Pages 1393-1406

  Neishtadt, Anatoly ^a   Vasiliev, Alexei ^a  

^a Russian Academy of Sciences   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 29744462617     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/18/3/023     Document Type: Article

References (20)

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3. Neishtadt A I 1975 Some resonant problems in nonlinear systems PhD Thesis Moscow State University, Moscow (in Russian)
4. Timofeev A V 1978 On the constancy of an adiabatic invariant when the nature of the motion changes Sov. Phys.-JETP 48 656-9
5. Gary J R, Escande D F and Tennyson J 1986 Adiabatic invariant change due to separatrix crossing Phys. Rev. A 34 4256-75
6. Neishtadt A I 1986 Change of an adiabatic invariant at a separatrix Sov. J. Plasma Phys. 12 568-73
7. Wiggins S 1988 Adiabatic chaos Phys. Lett. A128 339-42
8. Cary J R and Skodje R T 1989 Phase change between separatrix crossings Physica D 36 287-316
9. Elskens Y and Escande D F 1991 Slowly pulsating separatrices sweep homoclinic tangles where islands must be small: an extension of classical adiabatic theory Nonlinearity 4 615-67
10. Escande D F 1988 Plasma Theory and Nonlinear and Turbulent Processes in Physics (Kiev, 1987) ed V G Baryakhtar et al (Singapore: World Scientific) pp 398-430
11. Neishtadt A I, Sidorenko V V and Treschev D V1997 Stable periodic motions in the problem of passage through a separatrix Chaos 72-11
12. Neishtadt A I, Sidorenko V V and Treschev D V 2001 On stability islands in the domain of separatrix crossings Nonlinear Mechanics ed V M Matrosov et al (Moscow: Fizmatlit) pp 192-203 (in Russian)
13. Bourland F J and Haberman R1990 Separatrix crossing: time invariant potentials with dissipation SIAM J. Appl. Math. 50 1716-44
14. Bourland F J and Haberman R 1994 Connection across a separatrix with dissipation Stud. Appl. Math. 9195-124
15. Neishtadt A I 1987 On the change in the adiabatic invariant on crossing a separatrix in systems with two degrees of freedom PMM USSR 51 586-92
16. Wisdom J 1985 A perturbative treatment of motion near the 3/1 commensurability Icarus 63 272-89
17. Büchner J and Zelenyi L M 1989 Regular and chaotic charged particle motion in magnetotaillike field reversals, 1, Basic theory of trapped motion J. Geophys. Res. 94 11821-42
18. Neishtadt A I 1991 Probability phenomena due to separatrix crossing Chaos 142-8
19. Neishtadt A I and Sidorenko V V 2004 Wisdom system: dynamics in the adiabatic approximation Cel. Mech. Dynam. Astron. 90 307-30
20. Neishtadt A I, Simó C, Treschev D V and Vasiliev A A in preparation