2012/01/23 by B. Alarcon, Begoña Alarcón, Sofia B. S. D. Castro +6
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS
paper · pdf · doi:10.48550/arxiv.1201.4818
openalex publication_date 2012/01/23 · arxiv created 2012/06/27 · arxiv updated 2012/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
There are many tools for studying local dynamics. An important problem is how this information can be used to obtain global information. We present examples for which local stability does not carry on globally. To this purpose we construct, for any natural n>1, planar maps whose symmetry group is Zn having a local attractor that is not a global attractor. The construction starts from an example with symmetry group Z4. We show that although this example has codimension 3 as a Z4-symmetric map-germ, its relevant dynamic properties are shared by two 1-parameter families in its universal unfolding. The same construction can be applied to obtain examples that are also dissipative. The symmetry of these maps forces them to have rational rotation numbers.