Work

On the geometry of period doubling invariant sets for area-preserving maps

Year: 2025

Type: article

Abstract: The geometry of the period doubling Cantor sets of strongly dissipative infinitely renormalizable Hénon-like maps has been shown to be unbounded by M. Lyubich, M. Martens, and A. de Carvalho, although the measure of unbounded 'spots' in the Cantor set has been demonstrated to be zero.We show that an even more extreme situation takes places for infinitely renormalizable area-preserving Hénon-like maps: Both bounded and unbounded geometries exist on subsets of positive measure.

Source: Discrete and Continuous Dynamical Systems

DOI: 10.3934/dcds.2025082

Authors: Denis Gaidashev, Dan Lilja

Institution: Uppsala University

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Vetenskapsrådet

Award: Renormalization in hydrodynamic models