Abstract
The maximum Lyapunov exponent is computed numerically for the double-well oscillator in a heat bath. Positive exponents are found in a wide range of friction coefficients in the low-damping regime.
Similar content being viewed by others
References
H. A. Kramers,Physica 7:285 (1940).
P. Hänggi, P. Talkner, and M. Borkovec,Rev. Mod. Phys. 62:251 (1990).
J.-P. Eckmann and D. Ruelle,Rev. Mod. Phys. 57:617 (1985).
W. Ebeling, H. Herzel, W. Richert, and L. Schimansky-Geier,Z. Angew. Math. Mech. 66:141 (1986).
V. S. Anishchenko,Complex Oscillations in Simple Systems (Nauka, Moscow, 1990) [in Russian].
G. Mayer-Kress and H. Haken,J. Stat. Phys. 26:149 (1981).
J. F. Crutchfield, D. Farmer, and B. A. Huberman,Phys. Rep. 92:45 (1982).
H. Herzel, W. Ebeling, and Th. Schulmeister,Z. Naturforsch. 38a:1157 (1987).
V. S. Anishchenko and H. Herzel,Z. Angew. Math. Mech. 68:317 (1988).
A. R. Bulsara, E. W. Jacobs, and W. C. Schieve,Phys. Rev. A 48:4614 (1990).
K. Matsumoto and I. Tsuda,J. Stat. Phys. 31:87 (1983).
H. Herzel and B. Pompe,Phys. Lett. 122A:121 (1987).
H. Herzel,Z. Angew. Math. Mech. 68:382 (1988).
L. Arnold and V. Wikstütz, eds.,Lyapunov Exponents (Springer, Berlin, 1986).
W. Ebeling, H. Herzel, and L. Schimansky-Geier, inFrom Chemical to Biological Organization, M. Markus, S. C. Müller, and G. Nicolis, eds. (Springer, Berlin, 1988), p. 166.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Schimansky-Geier, L., Herzel, H. Positive Lyapunov exponents in the Kramers oscillator. J Stat Phys 70, 141–147 (1993). https://doi.org/10.1007/BF01053959
Issue Date:
DOI: https://doi.org/10.1007/BF01053959