We study diffusion and mixing in different linear fluid dynamics models, mainly related to
incompressible flows. In this setting, mixing is a purely advective effect that causes a transfer …

Mathematical study of scattering resonances | Bulletin of Mathematical Sciences Skip to main
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On July 9, 2001, Springer invited me to contribute a monograph on dynamical systems. I
immediately accepted, offering to write a book on dynamical zeta functions and dynamical …

Smooth mixing Anosov flows in dimension three are exponentially mixing Page 1 Annals of
Mathematics 197 (2023), 65–158 https://doi.org/10.4007/annals.2023.197.1.2 Smooth mixing …

We present a new scale U^ t, s _p U pt, s (s<-t< 0 s<-t< 0 and 1 ≤ p< ∞ 1≤ p<∞) of
anisotropic Banach spaces, defined via Paley–Littlewood, on which the transfer operator L …

The Sinai billiard map $ T $ on the two-torus, ie, the periodic Lorentz gas, is a discontinuous
map. Assuming finite horizon, we propose a definition $ h_* $ for the topological entropy of …

We prove that the geodesic flow on a geometrically finite locally symmetric space of negative
curvature is exponentially mixing with respect to the Bowen-Margulis-Sullivan measure. The …

We obtain an analog of the prime number theorem for a class of branched covering maps on
the 2-sphere S 2 called expanding Thurston maps, which are topological models of some …

We obtain an analog of the prime number theorem for a class of branched covering maps on
the 2-sphere S 2 called expanding Thurston maps, which are topological models of some …

We study a class of two-dimensional partially hyperbolic systems, not necessarily skew
products, in an attempt to develop a general theory. As a main result, we provide explicit …