A generalization of the Brouwer plane translation theorem

2024/08/15 by Wiseman, Jim
#37E30 (Primary) 37B20 (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2408.08183

Abstract

We show that if an orientation-preserving homeomorphism of the plane has a topologically chain recurrent point, then it has a fixed point, generalizing the Brouwer plane translation theorem.

Related

• Orientation Preserving Homeomorphisms of the Plane having BP-Chain Recurrent Points
• Three Brouwer fixed point theorems for homeomorphisms of the plane
• A new construction of counterexamples to the bounded orbit conjecture
• A foliated viewpoint on homotopy Brouwer theory
• Handel's fixed point theorem: A Morse theoretical point of view