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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the enhancement of diffusion by chaos,
escape rates and stochastic instability


Authors: Pierre Collet, Servet Martínez and Bernard Schmitt
Journal: Trans. Amer. Math. Soc. 351 (1999), 2875-2897
MSC (1991): Primary 58F11, 60J99
Published electronically: March 8, 1999
MathSciNet review: 1443868
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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: http://dx.doi.org/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
Published electronically: March 8, 1999
Article copyright: © Copyright 1999 American Mathematical Society