Renormalization of two-dimensional piecewise linear maps: Abundance of\n 2-D strange attractors

2017/03/11 by António Pumariño, Pumariño, Antonio, José Ángel Rodríguez +3
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Nonlinear Dynamics and Pattern Formation

paper · pdf · doi:10.48550/arxiv.1703.03964

openalex publication_date 2017/03/11 · openalex created_date 2022/09/27 · openalex updated_date 2026/07/28

Abstract

For a two parameter family of two-dimensional piecewise linear maps and for\nevery natural number n we prove not only the existence of intervals of\nparameters for which the respective maps are n times renormalizable but\nalso we show the existence of intervals of parameters where the coexistence of\nat least 2ⁿ strange attractors takes place. This family of maps contains\nthe two-dimensional extension of the classical one-dimensional family of tent\nmaps.\n

Related

• Abundance of weird quasiperiodic attractors in piecewise linear discontinuous maps
• On the emergence and properties of weird quasiperiodic attractors
• The bifurcation structure within robust chaos for two-dimensional piecewise-linear maps
• Towards a renormalization theory for quasi-periodically forced one dimensional maps III. Numerical Support
• Combinatorics, geometry and attractors of quasi-quadratic maps