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- HMAT HMAT, David Aubin, +15 authors Dominique Pestre
- 2002

Between the late 1960s and the beginning of the 1980s, the wide recognition that simple dynamical laws could give rise to complex behaviors was sometimes hailed as a true scientific revolution impacting several disciplines, for which a striking label was coined— " chaos. " Mathematicians quickly pointed out that the purported revolution was relying on the… (More)

Brillouin zones were introduced by Brillouin [Br] in the thirties to describe quantum mechanical properties of crystals, that is, in a lattice in R n. They play an important role in solid-state physics. It was shown by Bieberbach [Bi] that Brillouin zones tile the underlying space and that each zone has the same area. We generalize the notion of Brillouin… (More)

- Charles Pugh, Mauricio Matos Peixoto
- Scholarpedia
- 2008

In this note we consider the well known Hannay-Ozorio de Almeida sum formula from a mathematically rigorous viewpoint. In particular, we discuss situations where we can obtain the Sinai-Ruelle-Bowen measure as a limit taken over periodic orbits with periods in an interval which shrinks as it moves to infinity.

- Mauricio M Peixoto, Charles C Pugh
- Anais da Academia Brasileira de Ciências
- 2007

In Kupka et al. 2006 appears the Focal Stability Conjecture: the focal decomposition of the generic Riemann structure on a manifold M is stable under perturbations of the Riemann structure. In this paper, we prove the conjecture when M has dimension two, and there are no conjugate points.

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