Markov extensions, zeta functions, and Fredholm theory for piecewise invertible dynamical systems

Keller, G.

doi:10.1090/S0002-9947-1989-1005524-4

Markov extensions, zeta functions, and Fredholm theory for piecewise invertible dynamical systems
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by G. Keller

Trans. Amer. Math. Soc. 314 (1989), 433-497

DOI: https://doi.org/10.1090/S0002-9947-1989-1005524-4

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Abstract:

Transfer operators and zeta functions of piecewise monotonic and of more general piecewise invertible dynamical systems are studied. To this end we construct Markov extensions of given systems, develop a kind of Fredholm theory for them, and carry the results back to the original systems. This yields e.g. bounds on the number of ergodic maximal measures or equilibrium states.

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