相关论文: Almost reduction and perturbation of matrix cocycl…

We prove that Lyapunov exponents of typical H\"older continuous fiber bunched linear cocycles over singular hyperbolic flows have multiplicity 1: the subspace of exceptional cocycles has infinite codimension.

Given a locally constant linear cocycle over a subshift of finite type, we show that the existence of a uniform gap between the i-th and (i+1)-th Lyapunov exponents for all invariant measures implies the existence of a dominated splitting…

We show that typical (in the sense of Bonatti-Viana) H\"{o}lder and fiber-bunched $GL_d(\mathbb{R})$-valued cocycles over a subshift of finite type are uniformly quasi-multiplicative with respect to all singular value potentials. We prove…

Let $G$ be a semisimple Lie group acting on a space $X$, let $\mu$ be a compactly supported measure on $G$, and let $A$ be a strongly irreducible linear cocycle over the action of $G$. We then have a random walk on $X$, and let $T$ be the…

We consider Holder continuous fiber bunched GL(d,R)-valued cocycles over an Anosov diffeomorphism. We show that two such cocycles are Holder continuously cohomologous if they have equal periodic data, and prove a result for cocycles with…

We classify the GL(2,R)-invariant subvarieties M in strata of Abelian differentials for which any two M-parallel cylinders have homologous core curves. This answers a question of Mirzakhani and Wright. As a corollary we show that outside of…

We prove that a matrix from the split orthogonal group over a polynomial ring with coefficients in a small-dimensional ring can be reduced to a smaller matrix by a bounded number of elementary orthogonal transformations. The bound is given…

We study the implications of translation invariance on the tangent dynamics of extended dynamical systems, within a random matrix approximation. In a model system, we show the existence of hydrodynamic modes in the slowly growing part of…

We derive large deviations type (LDT) estimates for linear cocycles over an ergodic multifrequency torus translation. These models are called quasi-periodic cocycles. We make the following assumptions on the model: the translation vector…

Standard results from non-abelian cohomology theory specialize to a theory of torsors and stacks for cosimplicial groupoids. The space of global sections of the stack completion of a cosimplicial groupoid $G$ is weakly equivalent to the…

We present an analysis of one-dimensional models of dynamical systems that possess 'coherent structures'; global structures that disperse more slowly than local trajectory separation. We study cocycles generated by expanding interval maps…

We carry out extensive computer simulations to study the Lyapunov instability of a two-dimensional hard disk system in a rectangular box with periodic boundary conditions. The system is large enough to allow the formation of Lyapunov modes…

We use a Mayer-Vietoris-like spectral sequence to establish vanishing results for the cohomology of complements of linear and elliptic hyperplane arrangements, as part of a more general framework involving duality and abelian duality…

We prove a new characterization of uniform hyperbolicity for fiber-bunched cocycles. Specifically, we show that the existence of a uniform gap between the Lyapunov exponents of a fiber-bunched $SL(2,\mathbb{R})$-cocycle defined over a…

A general method to determine covariant Lyapunov vectors in both discrete- and continuous-time dynamical systems is introduced. This allows to address fundamental questions such as the degree of hyperbolicity, which can be quantified in…

We give a vanishing theorem for the monodromy eigenspaces of the Milnor fibers of complex line arrangements. By applying the modular bound of the local system cohomology groups given by Papadima-Suciu, the result is deduced from the…

The celebrated Oseledets theorem \cite{O}, building over seminal works of Furstenberg and Kesten on random products of matrices and random variables taking values on non-compact semisimple Lie groups \cite{FK,Furstenberg}, ensures that the…

For a cocycle of invertible real $n$-by-$n$ matrices, the Multiplicative Ergodic Theorem gives an Oseledets subspace decomposition of $\mathbb{R}^n$; that is, above each point in the base space, $\mathbb{R}^n$ is written as a direct sum of…

The Lyapunov exponents of GL(2)-cocycles over Markov shifts depend continuously on the underlying data, that is, on the matrix coefficients and the Markov measure transition probabilities.

We show the following geometric generalization of a classical theorem of W.H. Gottschalk and G.A. Hedlund: a skew action induced by a cocycle of (affine) isometries of a Hilbert space over a minimal dynamics has a continuous invariant…