For every positive integer r, we solve the modular Schwarzian differential equation {h,τ}=2π2r2E4, where E4 is weight 4 Eisenstein series, by means of equivariant functions on upper half-plane. This paper supplements previous works authors [20], [21], same has been solved for infinite families rational values r. also leads to solutions y″+r2π2E4y=0 These are quasi-modular forms SL2(Z) if r even...

We prove that there is a residual set of families of smooth or analytic unimodal maps with quadratic critical point and negative Schwarzian derivative such that almost every non-regular parameter is Collet-Eckmann with subexponential recurrence of the critical orbit. Those conditions lead to a detailed and robust statistical description of the dynamics. This proves the Palis conjecture in this ...

A model for computing image ow in image sequences containing a very wide range of instantaneous ows is proposed. This model integrates the spatio-temporal image derivatives from multiple temporal scales to provide both reliable and accurate instantaneous ow estimates. The integration employs robust regression and automatic scale weighting in a generalized brightness constancy framework. In addi...

We provide two new formulas for quasiconformal extension to C‾ harmonic mappings defined in the unit disk and having sufficiently small Schwarzian derivative. Both are generalizations of Ahlfors-Weill holomorphic functions.