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Markov extensions, zeta functions, and Fredholm theory for piecewise invertible dynamical systems. (English) Zbl 0686.58027
The author studies transfer operators and zeta functions of piecewise monotone and, more generally, on piecewise invertible dynamical systems. He constructs Markov extensions of the given system, develops a Fredholm theory for these extensions and these results are carried back to the original systems. This yields e.g. bounds on the number of ergodic maximal measures or equilibrium states.
Reviewer: N.Jacob

MSC:
37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
28D05 Measure-preserving transformations
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