The asymptotic stability of weakly perturbed two dimensional hamiltonian systems

Proceedings of the ASME Design Engineering Technical Conference

Volumn 6 C, Issue , 2001, Pages 2477-2486

  Arnold, Ludwig ^a   Imkeller, Peter ^b   Sri Namachchivaya, N ^c  

^a UNIVERSITY OF BREMEN   (Germany)

^b HUMBOLDT UNIVERSITY   (Germany)

^c UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; ASYMPTOTIC STABILITY; DAMPING; EQUATIONS OF MOTION; HAMILTONIANS; LYAPUNOV METHODS; OSCILLATORS (MECHANICAL); PERTURBATION TECHNIQUES; PROBABILITY DENSITY FUNCTION; RANDOM PROCESSES; SPECTRUM ANALYSIS; TWO DIMENSIONAL; DESIGN; LYAPUNOV FUNCTIONS; VIBRATIONS (MECHANICAL); WHITE NOISE;

EXPONENTIAL GROWTH RATE; KRAMERS OSCILLATOR; ADDITIVE WHITE NOISE; EXPONENTIAL GROWTH RATES; HAMILTONIAN SYSTEMS; INTENSITY NOISE; NOISE INTENSITIES; PERTURBATION APPROACH; SINGLE WELL; TOP LYAPUNOV EXPONENTS;

WHITE ACOUSTIC NOISE; HAMILTONIANS;

EID: 0035791074     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (18)

1. Arnold, L. Random Dynamical Systems. Springer-Verlag, Berlin 1998.
2. Arnold, L., Papanicolaou, G., and Wihstutz, V. Asymptotic Analysis of Lyapunov Exponent and Rotation Number of the Random Oscillator and Applications. SIAM Journal of Applied Mathematics, 46(3), 427-450, 1986
3. Arnold, L., and Wihstutz, V. Lyapunov Exponents, 1186, Lecture Notes in Mathematics, Springer Verlag: New York, 1986.
4. Arnold, L., and Imkeller, P. The Kramers oscillator revisited. In Stochastic Processes in Physics, Chemistry, and Biology, J. Freund, T. Pöschel, editors, Springer Lecture Notes in Physics, 557, 280-291, 2000.
5. Arnold, L., Imkeller, P., and Namachchivaya, N. Sri The Kramers Oscillator with Small Friction is Unstable. In preparation.
6. Arnold, V. I. Mathematical Methods of Classical Mechanics. Springer-Verlag, New York 1978.
7. Baxendale, P., and Goukasian, L. Lyapunov wxponents for small perturbations of Hamiltonian systems. Preprint, UCLA 2000.
8. Bolotin, V. V. Random Vibrations of Elastic Systems. Martinus Nijhoff Publishers, Boston, 1984.
9. Freidlin, M. I., and Wentzell, A. D. Random Perturbations of Dynamical Systems. 2nd edition. Springer-Verlag, Berlin 1998.
10. Freidlin, M. I. and Wentzell, A. D. Random Perturbations of Hamiltonian Systems. American Mathematical Society, Providence, RI, 1994.
11. Leng, G., and Namachchivaya, N. Sri, and Talwar, S. Robustness of Nonlinear Systems Perturbed by External Random Excitation. ASME Journal of Applied Mechanics, 59(4), 015-1022, 1992.
12. Imkeller, P., and Lederer, C. An explicit description of the Lyapunov exponents of the noisy damped harmonic oscillator. Dynamics and Stability of Systems, 14, 385-405, 1999.
13. Oseledec, V. I. A Multiplicative Ergodic Theorem. Lyapunov Characteristic Numbers for Dynamical Systems. Transaction of Moscow Mathematical Society, 19, 197-231, 1968.
14. Lin, Y. K., and Cai, G. Q. Probabilistic Theory of Structural Dynamics: Advanced Theory and Applications. McGraw-Hill, Inc, New York, 1995.
15. Namachchivaya, N. Sri, and Van Roessel, H. J. Maximal Lyapunov Exponent and Rotation Numbers for Two Coupled Oscillators Driven by Real Noise. Journal of Statistical Physics, 71(3/4), 549-567, 1993.
16. Pinsky, M., and Wihstutz, V. Lyapunov exponents of nilpotent Itô systems. Stochastics, 25, 43-57, 1988.
17. Schimansky-Geier, L., and Herzel, H. Positive Lyapunov exponents in the Kramers Oscillator. Journal of Statistical Physics, 782, 141-147, 1993.
18. Sowers, R. On the tangent flow of a stochastic differential equation with fast drift. Preprint, UIUC 1999.