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On the enhancement of diffusion by chaos, escape rates and stochastic instability
Author(s):
Pierre
Collet;
Servet
Martínez;
Bernard
Schmitt
Journal:
Trans. Amer. Math. Soc.
351
(1999),
2875-2897.
MSC (1991):
Primary 58F11, 60J99
Posted:
March 8, 1999
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Abstract:
We consider stochastic perturbations of expanding maps of the interval where the noise can project the trajectory outside the interval. We estimate the escape rate as a function of the amplitude of the noise and compare it with the purely diffusive case. This is done under a technical hypothesis which corresponds to stability of the absolutely continuous invariant measure against small perturbations of the map. We also discuss in detail a case of instability and show how stability can be recovered by considering another invariant measure.
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Additional Information:
Pierre
Collet
Affiliation:
C.N.R.S., Physique Théorique, Ecole Polytechnique, 91128 Palaiseau Cedex, France
Email:
collet@cpht.polytechnique.fr
Servet
Martínez
Affiliation:
Universidad de Chile, Facultad de Ciencias Físicas y Matemáticas, Departamento de Ingeniería Matemática, Casilla 170-3 Correo 3, Santiago, Chile
Email:
smartine@dim.uchile.cl
Bernard
Schmitt
Affiliation:
Université de Bourgogne, Département de Mathématiques, Faculté de Sciences Mirande, BP-138, 21004 Dijon Cedex, France
Email:
schmittb@satie.u-bourgogne.fr
DOI:
10.1090/S0002-9947-99-02023-1
PII:
S 0002-9947(99)02023-1
Received by editor(s):
May 1, 1996
Received by editor(s) in revised form:
January 23, 1997
Posted:
March 8, 1999
Copyright of article:
Copyright
1999,
American Mathematical Society
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