Coboundary equations of eventually expanding transformations

On Eventually Expanding Maps of the Interval

In this paper we conjecture that the piecewise linear map f(x) = px1I[0,1/p)(x)+ (sx − s/p)1I[1/p,1](x), p > 1, 0 < s < 1 which has an expanding, onto branch and a contracting branch is eventually piecewise expanding. We give a partial proof of the conjecture, in particular for values of p and s such that d− ln(p(1−s)+s) ln s e 6 = d− ln p ln s e.

Some examples of classical coboundary Lie bialgebras with coboundary duals

Some examples are given of finite dimensional Lie bialgebras whose brackets and cobrackets are determined by pairs of r-matrices. The aim of this Letter is to give some low-dimensional examples of classical coboundary Lie bialgebras [1, 2] with coboundary duals. Since such structures can be specified (up to automorphisms) by pairs of r-matrices, so it is natural to call them bi-r-matrix bialgeb...

Algebraic Transformations Ofpolynomial Equations

Crystals and Coboundary Categories

Following an idea of A. Berenstein, we define a commutor for the category of crystals of a finite dimensional complex reductive Lie algebra. We show that this endows the category of crystals with the structure of a coboundary category. Similar to the case of braided categories, there is a group naturally acting on multiple tensor products in coboundary categories. We call this group the cactus ...

Quenched stochastic stability for eventually expanding-on-average random interval map cocycles

The paper [FGTQ14] established fibrewise stability of random absolutely continuous invariant measures (acims) for cocycles of random Lasota-Yorke maps under a variety of perturbations, including “Ulam’s method”, a popular numerical method for approximating acims. The expansivity requirements of [FGTQ14] were that the cocycle (or powers of the cocycle) should be “expanding on average” before app...