A pre-Schwarzian and a Schwarzian derivative for locally univalent pluriharmonic mappings in Cn are introduced. Basic properties such as the chain rule, multiplicative invariance affine proved these operators. It is shown that stable only with respect to rotations of identity. characterization given case when holomorphic. Furthermore, it if mapping vanishes then analytic part this Möbius transf...

The role of Schwarzian derivative in the study nonlinear ordinary differential equations is revisited. Solutions and invariances admitted by Painlev\'e XXV-Ermakov equation, Ermakov equation third order linear a normal form are shown to be based on solutions equation. Starting from Riccati second element chian as simplest examples linearizable equations, introducing suitable change variables, i...

For a constant $alphain left(-frac{pi}{2},frac{pi}{2}right)$,  we definea  subclass of the spirallike functions, $SP_{p}(alpha)$, the setof all functions $fin mathcal{A}$[releft{e^{-ialpha}frac{zf'(z)}{f(z)}right}geqleft|frac{zf'(z)}{f(z)}-1right|.]In  the present paper, we shall give the estimate of the norm of the pre-Schwarzian derivative  $mathrm{T}...

In this paper we study measurable dynamics for the widest rea sonable class of smooth one dimensional maps Three principle de compositions are described in this class decomposition of the global measure theoretical attractor into primitive ones ergodic decompo sition and Hopf decomposition For maps with negative Schwarzian derivative this was done in the series of papers BL BL but the approach ...