Near invariance and local transience for random diffeomorphisms

For random diffeomorphisms depending on a parameter, nearly invariant sets are described via an associated deterministic control system. Conditions are provided guaranteeing that the system leaves the support of an invariant measure under small perturbations of the parameter and estimates for the exit times are given.

[1]  A. Bovier,et al.  Metastability in Reversible Diffusion Processes I: Sharp Asymptotics for Capacities and Exit Times , 2004 .

[2]  T. Gayer.  Control sets and their boundaries under parameter variation , 2004 .

[3]  Wolfgang Kliemann,et al.  On unique ergodicity for degenerate diffusions , 1987 .

[4]  Michael Dellnitz,et al.  Chapter 5 - Set Oriented Numerical Methods for Dynamical Systems , 2002 .

[5]  Fritz Colonius,et al.  Near Invariance for Markov Diffusion Systems , 2008, SIAM J. Appl. Dyn. Syst..

[6]  T. Gayer.  ON MARKOV CHAINS AND THE SPECTRA OF THE CORRESPONDING FROBENIUS–PERRON OPERATORS , 2001 .

[7]  Peter Deuflhard,et al.  Transfer Operator Approach to Conformational Dynamics in Biomolecular Systems , 2001 .

[8]  Matteo Turilli,et al.  Dynamics of Control , 2007, First Joint IEEE/IFIP Symposium on Theoretical Aspects of Software Engineering (TASE '07).

[9]  Philipp Metzner,et al.  Graph Algorithms for Dynamical Systems , 2006 .

[10]  Eduardo Sontag,et al.  Discrete-Time Transitivity and Accessibility: Analytic Systems , 1993 .

[11]  S. Meyn,et al.  Phase transitions and metastability in Markovian and molecular systems , 2004 .

[12]  Wolfgang Kliemann,et al.  Qualitative Theory of Stochastic Systems , 1983 .

[13]  G. Froyland.  Statistically optimal almost-invariant sets , 2005 .

[14]  A. Mielke.  Analysis, modeling and simulation of multiscale problems , 2006 .

[15]  A. Bovier,et al.  Metastability in reversible diffusion processes II. Precise asymptotics for small eigenvalues , 2005 .

[16]  Michael Dellnitz,et al.  Detecting and Locating Near-Optimal Almost-Invariant Sets and Cycles , 2002, SIAM J. Sci. Comput..

[17]  M. Freidlin,et al.  Random Perturbations of Dynamical Systems , 1984 .

[18]  A. J. Homburg,et al.  Bifurcations of stationary measures of random diffeomorphisms , 2005, Ergodic Theory and Dynamical Systems.

[19]  P. Deuflhard,et al.  Identification of almost invariant aggregates in reversible nearly uncoupled Markov chains , 2000 .

[20]  O. Junge,et al.  Almost Invariant Sets in Chua's Circuit , 1997 .