# American Institute of Mathematical Sciences

April  2018, 38(4): 2093-2123. doi: 10.3934/dcds.2018086

## Invariance entropy, quasi-stationary measures and control sets

 Institut für Mathematik, Universität Augsburg, Universitätsstrasse 14,86159 Augsburg, Germany

Received  May 2017 Revised  October 2017 Published  January 2018

Fund Project: Research supported by DFG grant 124/19-2

For control systems in discrete time, this paper discusses measure-theoretic invariance entropy for a subset Q of the state space with respect to a quasi-stationary measure obtained by endowing the control range with a probability measure. The main results show that this entropy is invariant under measurable transformations and that it is already determined by certain subsets of Q which are characterized by controllability properties.

Citation: Fritz Colonius. Invariance entropy, quasi-stationary measures and control sets. Discrete & Continuous Dynamical Systems - A, 2018, 38 (4) : 2093-2123. doi: 10.3934/dcds.2018086
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##### References:
Extremal graphs for (24) and the set $[d(\alpha),0.5]$ in $Q = [0.2,0.5\dot{]}$ (here $A = 0.05,\sigma = 0.1$ and $\alpha = 0.08$)
Extremal graphs for (44) and the $W$-control sets $D_1(\alpha) = [a(\alpha),b(\alpha))$ and $D_2(\alpha) = [d(\alpha),0.7)$ in $Q = [0.1,0.7\dot {]}$ (here $A = 0.05,\sigma = 0.1$ and $\alpha = 0.08$)
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