Rigorous computation of expansion in one-dimensional dynamics

2025/05/26 by Pilarczyk, Paweł, Palczewski, Michał, Luzzatto, Stefano
#37D20 #37E05 #65G30 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.20495

Abstract

We introduce an effective algorithmic method and its software implementation for rigorous numerical computation of a lower bound for uniform expansion in one-dimensional dynamics. The approach is based on interval arithmetic and efficient graph algorithms. We discuss and illustrate the effectiveness of our method and apply it to the quadratic map family.

Citations

• On parameter loci of the Hénon family
• Decidability of chaos for some families of dynamical systems
• INTERVAL METHODS FOR RIGOROUS INVESTIGATIONS OF PERIODIC ORBITS
• Almost every real quadratic map is either regular or stochastic

Related

• Expansion systems
• Recent progress in graph theory using expansion
• The Complexity of Approximating Vertex Expansion
• Approximation Theory and the Design of Fast Algorithms
• Discretization and Optimization using Graphs: One-Dimensional Algorithm