Conformally symplectic dynamics and symmetry of the Lyapunov spectrum

Communications in Mathematical Physics

Volumn 194, Issue 1, 1998, Pages 47-60

  Wojtkowski, Maciej P ^a   Liverani, Carlangelo ^b  

^a University of Arizona   (United States)

^b UNIVERSITY OF ROME TOR VERGATA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032474170     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050347     Document Type: Article

References (19)

1. Arnold, V.I.: Mathematical Methods in Classical Mechanics. Berlin-Heidelberg-New York: Springer Verlag, 1978
2. Abraham, R., Marsden, J.E., Ratiu, T.: Manifolds, tensor analysis and applications. Berlin-Heidelberg-New York: Springer Verlag, 1988
3. Benettin, G., Galgani, I., Giorgilli, A., Strelcyn, J.-M.: Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them. Meccanica 15, 9-20 (1980)
4. Bonetto, F., Gallavotti, G., Garrido, P.L.: Chaotic principle: An experimental test. Preprint (1996)
5. Choquard, Ph.: Lagrangian formulation of Nosé-Hoover and of isokinetic dynamics. ESI report (1996)
6. Chernov, N.I., Eyink, G.L., Lebowitz, J.L., Sinai, Ya.G.: Steady-state electric conduction in the periodic Lorentz gas. Commun. Math. Phys. 154, 569-601 (1993)
7. Dellago, C.P., Posch, H.A., Hoover, W.G.: Lyapunov instability in a system of hard disks in equilibrium and nonequilibrium steady states. Phys. Rev. E 53, n.2, 1485-1501 (1996)
8. Dettmann, C.P., Morriss, G.P.: Proof of Lyapunov exponent pairing for systems at constant kinetic energy. Phys. Rev. E 53, 5541 (1996)
9. Dettmann, C.P., Morriss, G.P.: Hamiltonian formulation of the Gaussian isokinetic thermostat. Phys. Rev. E 54, 2495 (1996)
10. Dettmann, C.P., Morriss, G.P.: Hamiltonian reformulation and pairing of Lyapunov exponents for Nosé-Hoover dynamics. Phys. Rev. E 55, 3693 (1997)
11. Evans, D.J., Cohen, E.G.D., Morriss, G.P.: Viscosity of a simple fluid from its maximal Lyapunov exponents. Physical Review 42A, 5990-5997 (1990)
12. Evans, D.J., Morriss, G.P.: Statistical Mechanics of nonequilibrium liquids. New York: Academic Press, 1990
13. Garrido, P.L., Gallavotti, G.: Billiards correlation functions. J. Stat. Phys. 76, 549-586 (1994)
14. Latz, A., van Beijeren, H., Dorfman, J.R.: Lyapunov spectrum and the conjugate pairing rule for a thermostatted random Lorentz gas: Kinetic theory. Preprint (1996)
15. Oseledets, V.I.: A multiplicative ergodic theorem: Characteristic Lyapunov exponents of dynamical systems. Trans. Moscow Math. Soc. 19, 197-231 (1968)
16. Ruelle, D.: Ergodic theory of differentiable dynamical systems. Publ. Math. IHES 50, 27-58 (1979)
17. Vaisman, I.: Locally conformal symplectic manifolds. Int. J. Math-Math. Sci. 8, 521-536 (1985)
18. Wojtkowski, M.P.: Measure Theoretic Entropy of the system of hard spheres. Ergodic Theory and Dynamical Systems. 8, 133-153 (1988)
19. Wojtkowski, M.P.: Systems of classical interacting particles with nonvanishing Lyapunov exponents. In: Lyapunov Exponents, Proceedings, Oberwolfach 1990, L. Arnold, H. Crauel, J.-P. Eckmann (Eds.), Lecture Notes in Math. Vol. 1486, 1991, pp. 243-262