On irreducibility of oseledets subspaces

On Hölder-continuity of Oseledets subspaces

For Hölder cocycles over a Lipschitz base transformation, possibly noninvertible, we show that the subbundles given by the Oseledets Theorem are Höldercontinuous on compact sets of measure arbitrarily close to 1. The results extend to vector bundle automorphisms, as well as to the Kontsevich-Zorich cocycle over the Teichmüller flow on the moduli space of abelian differentials. Following a recen...

On Aspects of Numerical Ergodic Theory: Stability of Ulam’s Method, Computing Oseledets Subspaces and Optimal Mixing

A dynamical system is a pairing between a set of states X ⊂ Rd and a map T : X which describes how the system evolves from state to state over time. The Perron– Frobenius, or transfer, operator is a natural extension of the point-by-point dynamics defined by T to an ensemble theory which describes the evolution of distributions of points. It features heavily in dynamical systems theory and in a...

On the Oseledets Regularity Functions

We investigate regularity functions corresponding to a fixed Lyapunov bundle E in the Oseledets multiplicative ergodic theorem for an ergodic flow or diffeomorphism. These functions measure the deviation of the growth in norm of the linearized system from constant exponential growth. In general, Oseledets regularity functions were only known to be Borel measurable. Our main result is that if E ...

Comment on frame's of subspaces

Irreducibility on General Fuzzy Automata

The aim of this paper is the study of a covering of a max-mingeneral fuzzy automaton by another, admissible relations, admissiblepartitions of a max-min general fuzzy automaton,$tilde{delta}$-orthogonality of admissible partitions, irreduciblemax-min general fuzzy automata. Then we obtain the relationshipsbetween them.