Asymptotic differentiable structure on Cantor set
type: Item
instance of: scholarly article
title: Asymptotic differentiable structure on Cantor set
zbMATH Open document ID: 0794.58014
DOI: 10.1007/BF02096725
author: Yunping Jiang
published in: Communications in Mathematical Physics
publication date: 1994-01-09T00:00:00Z
review text: The subject of the study are unimodal mappings of the interval for which the critical point either escapes to infinity (hyperbolic case) or is mapped to a fixed point in the second iterate (subhyperbolic case). In both cases the map exhibits full chaos. In the hyperbolic case, under sufficient smoothness conditions, the dynamics is expanding. However, the work only assumes \(C^{1+\alpha}\) smoothness and expansion is imposed by the condition that diameters of preimages of the natural Markov partition shrink exponentially fast. In the hyperbolic case, the scaling functions of resulting invariant Cantor sets are studied. Families of hyperbolic maps are then considered tending to a subhyperbolic one. A connection, rather a complicated one, is found between the limits of scaling functions and the orbifold structure of the limiting subhyperbolic map.
Mathematics Subject Classification ID: 37E99
Mathematics Subject Classification ID: 37D99
zbMATH DE Number: 459112
zbMATH Keywords: dual Cantor set
zbMATH Keywords: Markov partition
zbMATH Keywords: scaling functions
zbMATH Keywords: Cantor sets
zbMATH Keywords: hyperbolic maps
zbMATH Keywords: subhyperbolic
zbMATH Keywords: orbifold
reviewed by: Grzegorz Świątek
MaRDI profile type: Publication
cites work: Equilibrium states and the ergodic theory of Anosov diffeomorphisms
cites work: Q3816752
cites work: Three dimensional manifolds, Kleinian groups and hyperbolic geometry
full work available at URL: https://doi.org/10.1007/bf02096725
OpenAlex ID: W1998350389
description: scientific article; zbMATH DE number 459112