Invariant densities for dynamical systems with random switching

Yuri Bakhtin; Tobias Hurth

doi:10.1088/0951-7715/25/10/2937

Invariant densities for dynamical systems with random switching

Yuri Bakhtin, Tobias Hurth

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider a nonautonomous ordinary differential equation on a smooth manifold, with right-hand side that randomly switches between the elements of a finite family of smooth vector fields. For the resulting random dynamical system, we show that Hörmander type hypoellipticity conditions are sufficient for uniqueness and absolute continuity of an invariant measure.

Original language	English (US)
Pages (from-to)	2937-2952
Number of pages	16
Journal	Nonlinearity
Volume	25
Issue number	10
DOIs	https://doi.org/10.1088/0951-7715/25/10/2937
State	Published - Oct 2012

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Applied Mathematics

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title = "Invariant densities for dynamical systems with random switching",

abstract = "We consider a nonautonomous ordinary differential equation on a smooth manifold, with right-hand side that randomly switches between the elements of a finite family of smooth vector fields. For the resulting random dynamical system, we show that H{\"o}rmander type hypoellipticity conditions are sufficient for uniqueness and absolute continuity of an invariant measure.",

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AB - We consider a nonautonomous ordinary differential equation on a smooth manifold, with right-hand side that randomly switches between the elements of a finite family of smooth vector fields. For the resulting random dynamical system, we show that Hörmander type hypoellipticity conditions are sufficient for uniqueness and absolute continuity of an invariant measure.

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Invariant densities for dynamical systems with random switching

Abstract

ASJC Scopus subject areas

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