Yann Chaubet, Yannick Guedes Bonthonneau
Published 2022-11-16Version 1
Dynamical series such as the Ruelle zeta function have become a staple in the study of hyperbolic flows. They are usually analyzed by relating them to the resolvent of the vector field. In this paper we give the general form of such relations, which involves the intersection of the kernel of said resolvent with integration currents. Our formula is actually valid for any smooth flow, not necessarily hyperbolic. As an application, we introduce certain dynamical series that had not appeared before. Finally, we compute their value at zero, and their relation with topological invariants.
The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds
Two-parameter unfolding of a parabolic point of a vector field in $\mathbb C$ fixing the origin
On $C^r-$closing for flows on 2-manifolds
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