Dynamics near a class of nonhyperbolic fixed points

TL;DR

This paper studies the behavior of dynamical systems near nonhyperbolic fixed points, establishing new theorems on stable manifolds and degenerate Hartman phenomena, and discussing the finite shadowing property.

Contribution

It introduces new theorems on stable manifolds and degenerate Hartman phenomena near nonhyperbolic fixed points, expanding understanding of local dynamics.

Findings

Established a stable manifold theorem for nonhyperbolic fixed points.

Proved a degenerate Hartman theorem under certain conditions.

Discussed the finite shadowing property in this context.

Abstract

In this paper, we investigate some dynamical properties near a nonhyperbolic fixed point. Under some conditions on the higher nonlinear terms, we establish a stable manifold theorem and a degenerate Hartman theorem. Furthermore, the finite shadowing property also be discussed.