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5 papers · 2 filters
Continuity of Hausdorff Dimension Across Generic Dynamical Lagrange and Markov Spectra II
A. Cerqueira, C. G. Moreira, S. Romaña
Let be a smooth pinched negatively curved Riemannian metric on a complete surface , and let be a basic hyperbolic set of the geodesic flow of with Hausdorff di…
Livsic theorem for diffeomorphism cocycles
Artur Avila, Alejandro Kocsard, Xiao-Chuan Liu
We prove the so called Livšic theorem for cocycles taking values in the group of $C^{1+β}-diffeomorphisms of any closed manifold of arbitrary dimension. Since no localization hypot…
On bifurcation of eigenvalues along convex symplectic paths
Yinshan Chang, Yiming Long, Jian Wang
We consider a continuously differentiable curve in the space of real symplectic matrices, which is the solution of the following ODE: $\frac{\mathrm{d…
The set of fiber-bunched cocycles with nonvanishing Lyapunov exponents over a partially hyperbolic map is open
Lucas Backes, Mauricio Poletti, Adriana Sánchez
We prove that the set of fiber-bunched -valued Hölder cocycles with nonvanishing Lyapunov exponents over a volume preserving, accessible and center-bunched partia…
Complexity and fractal dimensions for infinite sequences with positive entropy
Carlos Gustavo Moreira, Christian Mauduit
The complexity function of an infinite word on a finite alphabet is the sequence counting, for each non-negative , the number of words of length on the alphabet …