Abstract:
The construction of reversible extensions of dynamical systems presented in a previous paper by the author and A. V. Lebedev is enhanced, so that it applies to arbitrary mappings (not necessarily with open range). It is based on calculating the maximal ideal space of C∗-algebras that extends endomorphisms to partial automorphisms via partial isometric representations, and involves a new set of ‘parameters’ (the role of parameters is played by chosen sets or ideals).
As model examples, we give a thorough description of reversible extensions of logistic maps and a classification of systems associated with compression of unitaries generating homeomorphisms of the circle.
Bibliography: 34 titles.
Keywords:
extensions of dynamical systems, logistic maps, partial isometry, C∗-algebra.
\Bibitem{Kwa12}
\by B.~K.~Kwa{\'s}niewski
\paper $C^*$-algebras associated with reversible extensions of logistic maps
\jour Sb. Math.
\yr 2012
\vol 203
\issue 10
\pages 1448--1489
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Linking options:
https://www.mathnet.ru/eng/sm7819
https://doi.org/10.1070/SM2012v203n10ABEH004271
https://www.mathnet.ru/eng/sm/v203/i10/p71
This publication is cited in the following 5 articles:
Kwasniewski B.K., Lebedev A., “Variational Principles For Spectral Radius of Weighted Endomorphisms of C(X, D)”, Trans. Am. Math. Soc., 373:4 (2020), 2659–2698
B. K. Kwaśniewski, “Crossed products by endomorphisms of C0(X)-algebras”, J. Funct. Anal., 270:6 (2016), 2268–2335
B. K. Kwaśniewski, “Ideal structure of crossed products by endomorphisms via reversible extensions of C∗-dynamical systems”, Internat. J. Math., 26:3 (2015), 1550022, 45 pp.
B. K. Kwaśniewski, “Extensions of C∗-Dynamical Systems to Systems with Complete Transfer Operators”, Math. Notes, 98:3 (2015), 419–428
B. K. Kwaśniewski, “Crossed products for interactions and graph algebras”, Integral Equations Operator Theory, 80:3 (2014), 415–451
Citation in format AMSBIB
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