Sets of vector fields with various properties of shadowing of pseudotra-jectories

TL;DR

This paper investigates the structure of vector fields with shadowing properties, identifying conditions under which their $C^1$-interiors are composed of structurally stable fields, thus advancing understanding of dynamical stability.

Contribution

It characterizes the $C^1$-interiors of sets of vector fields with shadowing properties and links these to structural stability under certain reparametrizations.

Findings

$C^1$-interiors of shadowing sets contain structurally stable fields under specific reparametrizations

The paper identifies classes of vector fields with shadowing properties that have stable $C^1$-interiors

Provides conditions under which shadowing properties imply structural stability

Abstract

We study the structure of $C^1$-interiors of sets of smooth vector fields with various properties of shadowing of pseudotrajectories. It is shown for which classes of reparametrizations of shadowing trajectories the corresponding interiors consist of structurally stable fields.