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Finite Gauss measure on the space of interval exchange transformations. Lyapunov exponents

Anton Zorich (1996)

Annales de l'institut Fourier

We construct a map on the space of interval exchange transformations, which generalizes the classical map on the interval, related to continued fraction expansion. This map is based on Rauzy induction, but unlike its relative kown up to now, the map is ergodic with respect to some finite absolutely continuous measure on the space of interval exchange transformations. We present the prescription for calculation of this measure based on technique developed by W. Veech for Rauzy induction.We study...

Finiteness problems on Nash manifolds and Nash sets

José F. Fernando, José Manuel Gamboa, Jesús M. Ruiz (2014)

Journal of the European Mathematical Society

We study here several finiteness problems concerning affine Nash manifolds M and Nash subsets X . Three main results are: (i) A Nash function on a semialgebraic subset Z of M has a Nash extension to an open semialgebraic neighborhood of Z in M , (ii) A Nash set X that has only normal crossings in M can be covered by finitely many open semialgebraic sets U equipped with Nash diffeomorphisms ( u 1 , , u m ) : U m such that U X = { u 1 u r = 0 } , (iii) Every affine Nash manifold with corners N is a closed subset of an affine Nash manifold...

Finsler Conformal Lichnerowicz-Obata conjecture

V. S. Matveev, H.-B. Rademacher, M. Troyanov, A. Zeghib (2009)

Annales de l’institut Fourier

We prove the Finsler analog of the conformal Lichnerowicz-Obata conjecture showing that a complete and essential conformal vector field on a non-Riemannian Finsler manifold is a homothetic vector field of a Minkowski metric.

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