The Lyapunov exponents of generic volume-preserving and symplectic maps

By Jairo Bochi, Marcelo Viana. 2005

205 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/4afab5e7e6f04e92c214eb401148d2bd0a566eb2

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In Computer Networks and Communications

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

On the regularization of conservative maps (2008, methodology): “Zehnder’s Theorem has been used in [3] and [5] to achieve this conclusion in the symplectic case, and such a result is necessary for the conclusion of the central dychotomy of [3].”
Continuity of Lyapunov exponents for random two-dimensional matrices (2016, background): “Moreover, this has been extended to cocycles and diffeomorphisms in arbitrary dimension, by Bochi and Viana [6, 7].”
Some characterizations of domination (2008, unknown): “D S] 3 1 A ug 2 00 8”
New criteria for ergodicity and nonuniform hyperbolicity (2009, methodology): “Viana [11], we can make a C(1) perturbation to obtain the following: (a) the center bundle has a dominated splitting E = E ⊕ E−, and (b) the sets C where λ(x) > 0, and C− where λ−(x) < 0 have positive measure.”
Extremal Lyapunov exponents: an invariance principle and applications (2010, result): “The results of Bochi [10, 11] and Bochi, Viana [12] show that continuity depends quite subtly on topology in the space of cocycles.”
A survey on partially hyperbolic dynamics (2006, unknown): “ either fhas a.e. zero exponents or fis Anosov In particular if the surface is not a torus then the generic fhas zero exponent. In [Boc], Jairo Bochi ﬁxed and completed the proof in [Ma3] and then in [BocVi], jointly with Marcelo Viana, they generalized the result to any dimension but loosing a litt”
C1 density of stable ergodicity (2017, result): “ends to the whole manifold. Such a set is constructed in [RRTU] for an open set of partially hyperbolic dieomorphims, dense among those with dim(Ec) = 2. This follows almost directly from results in [BV2] and [BaBo]. For the partially hyperbolic dieomorphisms with dim(Ec) >2, more delicate argume”
Complex one-frequency cocycles (2013, methodology): “tic functions A : R/Z → L(Cd,Cd) admitting a holomorphic extension to {|Imz| <δ} which is continuous up to the boundary. 1.2. Regularityanddomination. The proof of the Bochi-Viana Theorem given in [BV] centers around the idea that an absence of domination in the Oseledets splitting can be exploit”