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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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On the enhancement of diffusion by chaos, escape rates and stochastic instability
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by Pierre Collet, Servet Martínez and Bernard Schmitt PDF
Trans. Amer. Math. Soc. 351 (1999), 2875-2897 Request permission


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
  • Email:
  • 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
  • Email:
  • Bernard Schmitt
  • Affiliation: Université de Bourgogne, Département de Mathématiques, Faculté de Sciences Mirande, BP-138, 21004 Dijon Cedex, France
  • Email:
  • Received by editor(s): May 1, 1996
  • Received by editor(s) in revised form: January 23, 1997
  • Published electronically: March 8, 1999
  • © Copyright 1999 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 351 (1999), 2875-2897
  • MSC (1991): Primary 58F11, 60J99
  • DOI:
  • MathSciNet review: 1443868