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...

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 ...

We prove a criterion for the global stability of the positive equilibrium in discrete-time single-species population models of the form xn+1 = xnF (xn). This allows us to demonstrate analytically (and easily) the conjecture that local stability implies global stability in some well-known models, including the Ricker difference equation and a combination of the models by Hassel and Maynard Smith...

We gain further insight into the use of the Schwarzian derivative to obtain new results for a family of functional differential equations including the famous Wright’s equation and the Mackey-Glass type delay differential equations. We present some dichotomy results, which allow us to get easily computable bounds of the global attractor. We also discuss related conjectures, and formulate new op...