Complex bounds for multimodal maps: Bounded combinatorics

Nonlinearity

Volumn 14, Issue 5, 2001, Pages 1311-1330

  Smania, Daniel ^a  

^a IMPA   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040483441     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/14/5/320     Document Type: Article

References (14)

1. Blokh A and Lyubich M 1990 Measure and dimension of solenoidal attractors of one-dimensional dynamical systems Commun. Math. Phys. 127 573-83
2. de Faria E and de Melo W 2000 Rigidity of critical circle mappings II J. Am. Math. Soc. 13 343-70
3. de Melo W and van Strien S 1993 One-Dimensional Dynamics (New York: Springer)
4. Douady A and Hubbard J 1985 On the dynamics of polynomial-like mappings Ann. Sci. École Norm. Sup. (4) 18 287-343
5. Graczyk J and Swiatek G 1996 Polynomial-like property for real quadratic polynomials Topology Proc. 21 33-112
6. Hu J 1995 Renormalization, rigidity and universality in bifurcation theory PhD Thesis City University of New York
7. Hu J 1998 Bounded geometry in the supports of ergodic invariant probability measures Int. J. Bifurc. Chaos Appl. Sci. Eng. 8 1957-73
8. Kozlovski O 1998 Structural stability in one-dimensional dynamics PhD Thesis University of Amsterdam
9. Levin G and van Strien S 1998 Local connectivity of the Julia set of real polynomials Ann. Math. 147 471-541
10. LyubichM 1997 Dynamics of quadratic polynomials. I, II Acta Math. 178 185-297
11. Lyubich M and Yampolsky M 1997 Dynamics of quadratic polynomials: complex bounds for real maps Ann. Inst. Fourier (Grenoble) 47 1219-55
12. 2 multi-modal Collet-Eckmann maps without Schwarzian derivative assumptions Trans. Am. Math. Soc. 321 793-810
13. Smania D 2001 Renormalization theory for multimodal maps PhD Thesis IMPA
14. Sullivan D 1992 Bounds, quadratic differentials and renormalization conjectures AMS Centennial Publications: Mathematics into Twenty-first Century vol 2 (Providence, RI: American Mathematical Society)