Magnetic flows and Gaussian thermostats on manifolds of negative curvature

Maciej Wojtkowski

Fundamenta Mathematicae (2000)

  • Volume: 163, Issue: 2, page 177-191
  • ISSN: 0016-2736

Abstract

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We consider a class of flows which includes both magnetic flows and Gaussian thermostats of external fields. We give sufficient conditions for such flows on manifolds of negative sectional curvature to be Anosov.

How to cite

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Wojtkowski, Maciej. "Magnetic flows and Gaussian thermostats on manifolds of negative curvature." Fundamenta Mathematicae 163.2 (2000): 177-191. <http://eudml.org/doc/212437>.

@article{Wojtkowski2000,
abstract = {We consider a class of flows which includes both magnetic flows and Gaussian thermostats of external fields. We give sufficient conditions for such flows on manifolds of negative sectional curvature to be Anosov.},
author = {Wojtkowski, Maciej},
journal = {Fundamenta Mathematicae},
keywords = {magnetic flows; Gaussian thermostats; negative curvature; Anosov flows; Hamiltonian flow; symplectic structure},
language = {eng},
number = {2},
pages = {177-191},
title = {Magnetic flows and Gaussian thermostats on manifolds of negative curvature},
url = {http://eudml.org/doc/212437},
volume = {163},
year = {2000},
}

TY - JOUR
AU - Wojtkowski, Maciej
TI - Magnetic flows and Gaussian thermostats on manifolds of negative curvature
JO - Fundamenta Mathematicae
PY - 2000
VL - 163
IS - 2
SP - 177
EP - 191
AB - We consider a class of flows which includes both magnetic flows and Gaussian thermostats of external fields. We give sufficient conditions for such flows on manifolds of negative sectional curvature to be Anosov.
LA - eng
KW - magnetic flows; Gaussian thermostats; negative curvature; Anosov flows; Hamiltonian flow; symplectic structure
UR - http://eudml.org/doc/212437
ER -

References

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  1. [A-S] D. V. Anosov and Ya. G. Sinai, Certain smooth ergodic systems, Russian Math. Surveys 22 (1967), 103-167. 
  2. [B-C-P] F. Bonetto, E. G. D. Cohen and C. Pugh, On the validity of the conjugate pairing rule for Lyapunov exponents, J. Statist. Phys. 92 (1998), 587-627. Zbl0948.82024
  3. [B-G-M] F. Bonetto, G. Gentile and V. Mastropietro, Electric fields on a surface of constant negative curvature, Ergodic Theory Dynam. Systems, to appear. Zbl0959.37021
  4. [D-M] C. P. Dettmann and G. P. Morriss, Proof of Lyapunov exponent pairing for systems at constant kinetic energy, Phys. Rev. E 53 (1996), R5541-5544. 
  5. [E-C-M] D. J. Evans, E. G. D. Cohen and G. P. Morriss, Viscosity of a simple fluid from its maximal Lyapunov exponents, Phys. Rev. A 42 (1990), 5990-5997. 
  6. [Go] N. Gouda, Magnetic flows of Anosov type, Tôhoku Math. J. 49 (1997), 165-183. Zbl0938.37011
  7. [Gr] S. Grognet, Flots magnétiques en courbure négative, Ergodic Theory Dynam. Systems 19 (1999), 413-436. 
  8. [H] W. G. Hoover, Molecular Dynamics, Lecture Notes in Physics 258, Springer, 1986. Zbl0615.76004
  9. [K-B] A. Katok (in collaboration with K. Burns), Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dynamical systems, Ergodic Theory Dynam. Systems 14 (1994), 757-786. 
  10. [K-H] A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Cambridge Univ. Press, 1995. Zbl0878.58020
  11. [L-Y] F. Ledrappier and L.-S. Young, The metric entropy of diffeomorphisms: I. Characterization of measures satisfying Pesin's formula, II. Relations between entropy, exponents and dimension, Ann. of Math. 122 (1985), 509-539, 540-574. Zbl0605.58028
  12. [L] J. Lewowicz, Lyapunov functions and topological stability, J. Differential Equations 38 (1980), 192-209. Zbl0418.58012
  13. [P-P] G. P. Paternain and M. Paternain, Anosov geodesic flows and twisted symplectic structures, in: Dynamical Systems (Montevideo, 1995), Pitman Res. Notes Math. 362, Longman, 1996, 132-145. Zbl0868.58062
  14. [R] D. Ruelle, Positivity of entropy production in nonequilibrium statistical mechanics, J. Statist. Phys. 85 (1996), 1-23. Zbl0973.37014
  15. [V] I. Vaisman, Locally conformal symplectic manifolds, Internat. J. Math. Math. Sci. 8 (1985), 521-536. Zbl0585.53030
  16. [W] M. P. Wojtkowski, Systems of classical interacting particles with nonvanishing Lyapunov exponents, in: Lecture Notes in Math. 1486, Springer, 1991, 243-262. Zbl0744.58023
  17. [W-L] M. P. Wojtkowski and C. Liverani, Conformally symplectic dynamics and symmetry of the Lyapunov spectrum, Comm. Math. Phys. 194 (1998), 47-60. Zbl0951.37016

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