Invariant densities for dynamical systems with random switching

Yuri Bakhtin, Tobias Hurth

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)2937-2952
Number of pages16
JournalNonlinearity
Volume25
Issue number10
DOIs
StatePublished - Oct 2012

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Hypoellipticity
Random Dynamical Systems
Nonautonomous Differential Equations
Absolute Continuity
Smooth Manifold
uniqueness
Invariant Measure
Ordinary differential equations
continuity
dynamical systems
Vector Field
Switch
Dynamical systems
Ordinary differential equation
differential equations
Uniqueness
switches
Dynamical system
Switches
Sufficient

ASJC Scopus subject areas

  • Applied Mathematics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Invariant densities for dynamical systems with random switching. / Bakhtin, Yuri; Hurth, Tobias.

In: Nonlinearity, Vol. 25, No. 10, 10.2012, p. 2937-2952.

Research output: Contribution to journalArticle

Bakhtin, Yuri ; Hurth, Tobias. / Invariant densities for dynamical systems with random switching. In: Nonlinearity. 2012 ; Vol. 25, No. 10. pp. 2937-2952.
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