Some open problems in low dimensional dynamical systems

TL;DR

This paper presents a curated list of 33 open problems in low-dimensional dynamical systems, aiming to stimulate research and progress in areas like differential equations, stability, and geometric questions.

Contribution

It compiles and highlights unresolved problems across various topics in low-dimensional dynamical systems, encouraging further investigation and potential solutions.

Findings

Identification of 33 open problems in dynamical systems

Encourages research on differential equations and stability

Provides a resource for future mathematical exploration

Abstract

The aim of this paper is to share with the mathematical community a list of 33 problems that I have found along the years during my research. I believe that it is worth to think about them and, hopefully, it will be possible either to solve some of the problems or to make some substantial progress. Many of them are about planar differential equations but there are also questions about other mathematical aspects: Abel differential equations, difference equations, global asymptotic stability, geometrical questions, problems involving polynomials or some recreational problems with a dynamical component.