Reversible extensions of irreversible dynamical systems: the $C^*$-method

B. K. Kwaśniewski   ; A. V. Lebedev

Sbornik. Mathematics, Tome 199 (2008) no. 11, pp. 1621-1648

Résumé

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.

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