Average exit time for volume-preserving maps

Chaos

Volumn 7, Issue 1, 1997, Pages 139-147

  Meiss, J D ^a  

^a UNIVERSITY OF COLORADO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21744449703     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.166245     Document Type: Article

References (29)

1. C. F. F. K. Kamey, A. B. Rechester, and R. B. White, "Effect of noise on the standard mapping," Physica D 4, 425-438 (1982).
2. R. S. MacKay, J. D. Meiss, and I. C. Percival, "Transport in Hamiltonian systems," Physica D 13, 55-81 (1984).
3. J. D. Hanson, J. R. Gary, and J. D. Meiss, "Algebraic decay in self-similar Markov chains," J. Stat. Phys. 39, 327-345 (1985).
4. A. J. Lichtenbcrg, M. A. Lieberman, and N. W. Murray, "The effect of quasi-accelerator modes on diffusion," Physica D.28, 371-81 (1987).
5. V. Rom-Kedar and S. Wiggins, "Transport in two-dimensional maps," Arc. Rat. Mech. Anal. 109, 239-298 (1988).
6. T. Horita, H. Hata, R. Ishizaki, and H. Mori, "Long-time correlations and expansion-rate spectra of chaos in Hamiltonian systems," Prog. Theor. Phys. 83, 1065-1070 (1990).
7. R. Ishizaki, H. Hâta, T. Horita, and H. Mori, "Long-time correlations and anomalous diffusion due to accelerator modes in the standard maps," Prog. Theor. Phys. 84, 179-184 (1990).
8. R. Ishizaki, T. Horita, T. Kobayashi, and H. Mori, "Anomalous diffusion due to accelerator modes in the standard map," Prog. Theor. Phys. 85, 1013-1022 (1991).
9. R. W. Easton, "Transport through chaos," Nonlinearity 4, 583-590 (1991).
10. S. Wiggins, Chaotic Transport in Dynamical Systems, Interdisciplinary Applied Mathematics (Springer-Verlag, New York, 1991).
11. J. D. Meiss, "Symplectic maps, variational principles, and transport," Rev. Mod. Phys. 64, 795-848 (1992).
12. I2R. W. Easton, "Transport of phase space volume near isolated invariant sets," J. Dyn. Diff. Eq. 5, 529-535 (1993).
13. A. N. Yannacopoulos and G. Rowlands, "A model for the coexistence of diffusion and accelerator modes in a chaotic area-preserving map," J. Phys. A 26, 6231-6249 (1993).
14. R. W. Easton, J. D. Meiss, and S. Carver, "Exit times and transport for symplcctic twist maps," Chaos 3, 153-165 (1993).
15. M. Kac, "On the notion of recurrence in discrete stochastic processes," Bull. Am. Math. Soc. 53, 1002-1010 (1947).
16. M. Kac, Probability and Related Topics in Physical Sciences, Lecture in Applied Mathematics, Proceedings for the Summer Seminar in Boulder, Colorado (Interscience, New York, 1957).
17. M. Hénon, "Numerical study of quadratic area-preserving mappings," Q. J. Appl. Math. 27, 291-312 (1969).
18. S. R. Channon and J. L. Lebowitz, "Numerical experiments in stochasticity and heteroclinic oscillation," Nonlinear Dynamics, edited by R. H. G. Helleman (New York Academy of Science, New York, 1980), pp. 108-118.
19. C. F. F. K. Karney, "Long time correlations in the stochastic regime," Physica D 8, 360-380 (1983).
20. B. V. Chirikov and D. L. Shepelyansky, "Correlation properties of dynamical chaos in Hamiltonian systems," Physica D 13, 395-400 (1984).
21. Y. C. Lai, M. Ding, C. Grebogi, and R. Bliimel, "Algebraic decay and fluctuations of the decay exponent in Hamiltonian systems," Phys. Rev. A 48, 4661-4669 (1992).
22. N. Murray, "Critical function for the standard map," Physica D 52, 220-245 (1991).
23. G. M. Zaslavsky, and M. K. Tippelt, "Connection between recurrence-time statistics and anomalous transport," Phys. Rev. Lett. 67, 3251-3254 (1991).
24. R. S. MacKay, "Transport in 3D volume-preserving flows," J. Nonlinear Sei. 4, 329-354 (1994).
25. V. Rom-Kedar, A. Leonard, and S. Wiggins, "An analytical study of transport, mixing, and chaos in an unsteady vortical flow," J. Fluid Mech. 214, 347-394 (1990).
26. V. Rom-Kedar, "Transport rates of a class of two-dimensional maps and flows," Physica D 43, 229-268 (1990).
27. R. S. MacKay, J. D. Meiss, and I. C. Percival, "Resonances in area preserving maps," Physica D 27, 1-20 (1987).
28. V. G. Gelfreich, V. F. Lazutkin, and M. B. Tabanov, "Exponentially small splittings in Hamiltonian systems," Chaos 1, 137-142 (1991)
29. J. K. Moser, "On quadratic symplectic mappings," Math. Z. 216, 417-430 (1994).