Geodesic
Reversible extensions of irreversible dynamical systems: the $C^*$-method
Sbornik. Mathematics, Tome 199 (2008) no. 11, pp. 1621-1648

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A construction of a reversible extension of irreversible dynamical systems is presented. It is based on calculating the maximal ideal spaces of the $C^*$-algebras generated by these systems and the corresponding reversible extensions of endomorphisms. Connections between the objects that arise and dynamical systems of Smale horseshoe and other types are revealed. Bibliography: 20 titles. 
@article{SM_2008_199_11_a2,
     author = {B. K. Kwa\'sniewski and A. V. Lebedev},
     title = {Reversible extensions of irreversible dynamical systems: the $C^*$-method},
     journal = {Sbornik. Mathematics},
     pages = {1621--1648},
     publisher = {mathdoc},
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     number = {11},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2008_199_11_a2/}
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B. K. Kwaśniewski; A. V. Lebedev. Reversible extensions of irreversible dynamical systems: the $C^*$-method. Sbornik. Mathematics, Tome 199 (2008) no. 11, pp. 1621-1648. http://geodesic.mathdoc.fr/item/SM_2008_199_11_a2/