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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
MR Author ID: 50610

Servet Martínez
Affiliation: Universidad de Chile, Facultad de Ciencias Físicas y Matemáticas, Departamento de Ingeniería Matemática, Casilla 170-3 Correo 3, Santiago, Chile
MR Author ID: 120575

Bernard Schmitt
Affiliation: Université de Bourgogne, Département de Mathématiques, Faculté de Sciences Mirande, BP-138, 21004 Dijon Cedex, France

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