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math.DS2026
Margulis Measures on Expanding Foliations: Construction and Rigidity
Jérôme Buzzi, Yi Shi, Fan Yang +1
Given a diffeomorphism preserving a one-dimensional expanding foliation with homogeneous exponential growth, we construct a family of reference measures on each leaf o…
math.DS2026
Discontinuity of Lyapunov exponents vs Entropy for smooth surface diffeomorphisms
Jérôme Buzzi
Lyapunov exponents are fundamental invariants in smooth ergodic theory describing the asymptotic infinitesimal behavior along typical orbits. This text aims to explain how and why…
math.DS2026
Chaos on surfaces and beyond: a new notion of dynamical hyperbolicity
Jérôme Buzzi
We present some developments in the study of chaotic dynamics following the solution of a conjecture of Newhouse on the measures maximizing the entropy of smooth surface diffeomorp…