Aleksey A. Petrov, Sergei Yu. Pilyugin
Published 2014-02-23Version 1
In 1994, Sakai introduced the property of $C^0$ transversality for two smooth curves in a two-dimensional manifold. This property was related to various shadowing properties of dynamical systems. In this short note, we generalize this property to arbitrary continuous mappings of topological spaces into topological manifolds. We prove a sufficient condition for the $C^0$ transversality of two submanifolds of a topological manifold and a necessary condition of $C^0$ transversality for mappings of metric spaces into $\mathbb{R}^n$.
A sufficient condition for bifurcation in random dynamical systems
Self-inverses in Rauzy Classes
On $g$-functions for subshifts
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