Coherent structures and isolated spectrum for Perron–Frobenius cocycles

Coherent structures and isolated spectrum for Perron–Frobenius cocycles

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 and the rates of decay for functions of bounded variation under the action of the associated Perron–Frobenius cocycles. We prove that when the generators are ...

Regular Cocycles and Biautomatic Structures

In [ECHLPT] and [S] it is shown that if the fundamental group of a Seifert fibred 3manifold is not virtually nilpotent then it has an automatic structure. In the unpublished 1992 preprint [G2] Gersten constructs a biautomatic structure on the fundamental group of any circle bundle over a hyperbolic surface. He asks if the same can be done for the above Seifert fibered 3-manifold. We show the ex...

Cocycles, Symplectic Structures and Intersection

- Generic Cocycles Have One - Point Lyapunov Spectrum

We show the sum of the first k Lyapunov exponents of linear cocycles is an upper semicontinuous function in the L topologies, for any 1 ≤ p ≤ ∞ and k. This fact, together with a result from Arnold and Cong, implies that the Lyapunov exponents of the L-generic cocycle, p < ∞, are all equal.

Coherent imaging of periodic thick fine isolated structures

Publisher's statement This paper was published in Journal of the Optical Society of America A and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/abstract.cfm?URI=josaa-10-4614. Systematic or multiple reproduction or distribution to multiple locations via electronic or other mean...