Explosion of Smoothness for Conjugacies Between Unimodal Maps

• Type: Article in International Conference Proceedings Book
• Date: 2011

Authors

Jose F Alves (Author) FCUP; Vilton Pinheiro (Author) Other; Alberto A Pinto (Author) FCUP

Conference proceedings International

Title: Springer Proceedings in Mathematics

Pages: 115-119

International Conference DYNA 2008

Braga, PORTUGAL, SEP 08-12, 2008

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 1 Citation

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-002-WHP

DOI: 10.1007/978-3-642-14788-3_8

Resumo (PT): Let f and g be C r unimodal maps, with r ≥ 3, topologically conjugated by h and without periodic attractors. If h is differentiable at a point p in the expanding set E(f), with h′(p)≠0, then, there is an open renormalization interval J such that h is a C r diffeomorphism in the basin B(J) of J, and h is not differentiable at any point in I ∖ B(J). The expanding set E(f) contains all points with positive Lyapunov exponent, and if f has a Milnor’s interval cycle attractor A then E(f) has full Lebesgue measure.

Abstract (EN): Let f and g be C-r unimodal maps, with r >= 3, topologically conjugated by h and without periodic attractors. If h is strongly differentiable at a point p in the expanding set E(f), with h'(p) not equal 0, then, there is an open renormalization interval J such that h is a C-r diffeomorphism in the basin B(J) of J, and h is not strongly differentiable at any point in I \ B(J). The expanding set E(f) contains all points with positive Lyapunov exponent, and if f has a Milnor's interval cycle attractor A then E(f) has full Lebesgue measure.

Language: English

Type (Professor's evaluation): Scientific

Notes: http://www.springerlink.com/content/t333876434274k71/

No. of pages: 5