Interval Methods for Fixed and Periodic Points: Development and Visualization

José Eduardo de Almeida Ayres (IMPA, Brazil)

Luiz Henrique de Figueiredo (IMPA, Brazil)

Abstract: We describe the development of rigorous numerical methods based on interval analysis for finding all fixed points of a map and all attracting periodic points of a complex polynomial. We also discuss their performance with instructive visualizations.

Keywords: computer-assisted proofs, fixed points, interval analysis

Categories: G.1.2, G.1.5