Dynamical Zeta Functions and Dynamical Determinants for Hyperbolic Maps (eBook, PDF)
Viviane Baladi
eBook, PDF

Dynamical Zeta Functions and Dynamical Determinants for Hyperbolic Maps (eBook, PDF)

A Functional Approach

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The spectra of transfer operators associated to dynamical systems, when acting on suitable Banach spaces, contain key information about the ergodic properties of the systems. Focusing on expanding and hyperbolic maps, this book gives a self-contained account on the relation between zeroes of dynamical determinants, poles of dynamical zeta functions, and the discrete spectra of the transfer operators.In the hyperbolic case, the first key step consists in constructing a suitable Banach space of anisotropic distributions. The first part of the book is devoted to the easier case of expanding endom...

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