Abstract
We consider a Piecewise Deterministic Markov Process given by random switching between finitely many vector fields vanishing at [Formula: see text]. It has been shown recently that the behavior of this process is mainly determined by the signs of Lyapunov exponents. However, results have only been given when all these exponents have the same sign. In this paper, we consider the degenerate case where the process leaves invariant some face and results are stated when the Lyapunov exponents are of opposite signs. Our results enable in particular to close a gap in a discussion on random switching between two Lorenz vector fields by Bakhtin and Hurth, Invariant densities for dynamical systems with random switching, Nonlinearity 25 (2012) 2937–2952.
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