Sustainable dynamical systems

John Erik Fornæss

doi:10.3934/dcds.2003.9.1361

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2003, Volume 9, Issue 6: 1361-1386. Doi: 10.3934/dcds.2003.9.1361

This issue Previous Article Next Article Dispersive estimate for the wave equation with the inverse-square potential

Sustainable dynamical systems

John Erik Fornæss^1,

1.
Department of Mathematics, University of Michigan, East Hall 525, East University Avenue, Ann Arbor, MI 48109-1109

Received: July 2002

Revised: August 2003

Published: November 2003

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Abstract

In this paper we investigate randomly perturbed orbits. If a dynamical system is hyperbolic one can keep random perturbations from accumulating into large deviations by making small corrections. We study the converse problem. This leads naturally to the notion of sustainable orbits.

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Mathematics Subject Classification: Primary: 32H50; Secondary: 37A25.

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