Bulletin of the Belgian Mathematical Society - Simon Stevin
- Bull. Belg. Math. Soc. Simon Stevin
- Volume 15, Number 5 (2008), 789-796.
Rigidity in Dynamics
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.
Bull. Belg. Math. Soc. Simon Stevin, Volume 15, Number 5 (2008), 789-796.
First available in Project Euclid: 5 December 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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