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Stochastic stability of generalized SRB measures of Axiom A basic sets
Author(s):
Liu
Pei-Dong;
Zheng
Hong-Wen
Journal:
Proc. Amer. Math. Soc.
128
(2000),
3541-3545.
MSC (2000):
Primary 37D20
Posted:
May 18, 2000
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Abstract:
In this note we prove that the generalized SRB measure of an Axiom A basic set is stable under random diffeomorphisms type perturbations.
References:
-
- 1.
- L. Arnold, Random Dynamical Systems, Springer-Verlag, Berlin Heidelberg New York, 1998.
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- T. Bogenschütz, Private communication.
- 3.
- T. Bogenschütz, Stochastic stability of equilibrium states, Random Comput. Dynam. 4 (1996), 85-98. MR 97c:58085
- 4.
- T. Bogenschütz, Equilibrium states for random dynamical systems, Ph.D. Thesis, Bremen University, 1993.
- 5.
- P.-D. Liu, Random perturbations of Axiom A basic sets, J. Stat. Phys. 90(1/2) (1998), 467-490. MR 99a:58108
- 6.
- P.-D. Liu, M. Qian, Smooth Ergodic Theory of Random Dynamical Systems, Lec. Not. Math. 1606, Springer, 1995. MR 96m:58139
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- L.-S. Young, Stochastic stability of hyperbolic attractors, Ergod. Theory Dynam. Syst. 6 (1986), 311-319. MR 88a:58160
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Additional Information:
Liu
Pei-Dong
Affiliation:
Department of Mathematics and Institute of Mathematics, Peking University, Beijing 100871, People's Republic of China
Email:
lpd@pku.edu.cn
Zheng
Hong-Wen
Affiliation:
Department of Mathematics, Hebei Normal University, Shijiazhuang City 050016, Hebei, People's Republic of China
DOI:
10.1090/S0002-9939-00-05780-4
PII:
S 0002-9939(00)05780-4
Keywords:
Axiom A basic set,
generalized SRB measure,
random dynamical system
Received by editor(s):
January 28, 1999
Posted:
May 18, 2000
Additional Notes:
The first author was supported by the NSPCP and a fund from the NECC
The second author was supported by the National Natural Science Foundation of China.
Communicated by:
Michael Handel
Copyright of article:
Copyright
2000,
American Mathematical Society
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