On the eigenvalues of a renormalization operator

Nonlinearity

Volumn 16, Issue 5, 2003, Pages 1565-1571

  Yampolsky, Michael ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0142230397     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/16/5/301     Document Type: Article

References (12)

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3. [DH1] Douady A and Hubbard J H 1984 Etude dynamique des polynômes complexes, I-II. Pub. Math. d'Orsay
4. [EY] Epstein A and Yampolsky M 2003 The universal parabolic map Ergodic Theory Dyn. Syst. at press
5. [GSK] Gol'berg A I, Sinai Ya G and Khanin K M 1983 Universal properties of sequences of period-tripling bifurcations Usp. Mat. Nauk 38 187-8 (in Russian)
6. [Hin] Hinkle B 2000 Parabolic limits of renormalization Ergodic Theory Dyn. Syst. 20 173-229
7. [LY] Lyubich M and Yampolsky M 1997 Dynamics of quadratic polynomials: complex bounds for real maps Ann. Inst. Fourier 47 1219-55
8. [Sh] Shishikura M 1998 The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets Ann. Math. 147 225-67
9. [Ya1] Yampolsky M 2001 The attractor of renormalization and rigidity of towers of critical circle maps Commun. Math. Phys. 218 537-68
10. [Ya2] Yampolsky M 2003 Hyperbolicity of renormalization of critical circle maps Publ. Math. IHES at press
11. [Ya3] Yampolsky M 2003 Renormalization horseshoe of critical circle maps Commun. Math. Phys. at press
12. [Ya4] Yampolsky M 2002 Complex a priori bounds revisited Preprint (available from http://www.math.toronto.edu/̃yampol)