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Article Dans Une Revue Journal of Spectral Theory Année : 2020

Local and global trace formulae for smooth hyperbolic diffeomorphisms

Résumé

We define and study local and global trace formulae for discrete-time uniformly hyperbolic weighted dynamics. We explain first why dynamical determinants are particularly convenient tools to tackle this question. Then we construct counter-examples that highlight that the situation is much less well-behaved for smooth dynamics than for real-analytic ones. This suggests to study this question for Gevrey dynamics. We do so by constructing an anisotropic space of ultradistributions on which a transfer operator acts as a trace class operator. From this construction, we deduce trace formulae for Gevrey dynamics, as well as bounds on the growth of their dynamical determinants and the asymptotics of their Ruelle resonances.

Dates et versions

hal-03180696 , version 1 (25-03-2021)

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Malo Jézéquel. Local and global trace formulae for smooth hyperbolic diffeomorphisms. Journal of Spectral Theory, 2020, 10 (1), pp.185-249. ⟨10.4171/JST/290⟩. ⟨hal-03180696⟩
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