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Invariance entropy for topological semigroup actions


Authors: Fritz Colonius, Ryuichi Fukuoka and Alexandre J. Santana
Journal: Proc. Amer. Math. Soc. 141 (2013), 4411-4423
MSC (2010): Primary 54H15; Secondary 37B40, 93C25
DOI: https://doi.org/10.1090/S0002-9939-2013-11705-3
Published electronically: August 20, 2013
MathSciNet review: 3105883
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Abstract: Invariance entropy for the action of topological semigroups acting on metric spaces is introduced. It is shown that invariance entropy is invariant under conjugations and a lower bound and upper bounds of invariance entropy are obtained. The special case of control systems is discussed.


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Additional Information

Fritz Colonius
Affiliation: Institut für Mathematik, Universität Augsburg, Augsburg, Germany

Ryuichi Fukuoka
Affiliation: Departamento de Matemática, Universidade Estadual de Maringá, Maringá, Brazil

Alexandre J. Santana
Affiliation: Departamento de Matemática, Universidade Estadual de Maringá, Maringá, Brazil

DOI: https://doi.org/10.1090/S0002-9939-2013-11705-3
Keywords: Invariance entropy, semigroup actions, weak invariance
Received by editor(s): August 11, 2011
Received by editor(s) in revised form: February 12, 2012
Published electronically: August 20, 2013
Additional Notes: The research of the first author was partially supported by DFG grant Co 124/17-2 within DFG Priority Program 1305 Control Theory of Digitally Networked Dynamical Systems
The research of the second author was partially supported by the CNPq Grant 305557/2009-2
The research of the third author was partially supported by the Fundação Araucária Grant 496/10
Communicated by: Yingfei Yi
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.