Bulletin of the Belgian Mathematical Society - Simon Stevin

Rigidity in Dynamics

W. de Melo

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Abstract

In this paper we will review several results of rigidity in one-dimensional dynamics and its relation to renormalization. In many one dimensional dynamical systems the existence of a topological conjugacy between two mappings implies that the restriction of the conjugacy to the attractor extends to a smooth mapping. Thus the combinatorics imposes severe restrictions on the geometry of the attractor.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 15, Number 5 (2008), 789-796.

Dates
First available in Project Euclid: 5 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1228486407

Digital Object Identifier
doi:10.36045/bbms/1228486407

Mathematical Reviews number (MathSciNet)
MR2484132

Zentralblatt MATH identifier
1153.37370

Subjects
Primary: 37E05: Maps of the interval (piecewise continuous, continuous, smooth)
Secondary: 37F45: Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations 30D05: Functional equations in the complex domain, iteration and composition of analytic functions [See also 34Mxx, 37Fxx, 39-XX]

Keywords
rigidity renormalization smooth conjugacy

Citation

de Melo, W. Rigidity in Dynamics. Bull. Belg. Math. Soc. Simon Stevin 15 (2008), no. 5, 789--796. doi:10.36045/bbms/1228486407. https://projecteuclid.org/euclid.bbms/1228486407


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