Polynomial diffeomorphisms of C2: V. Critical points and Lyapunov exponents

Journal of Geometric Analysis

Volumn 8, Issue 3, 1998, Pages 349-383

  Bedford, Eric ^a   Smillie, John ^b  

^a INDIANA UNIVERSITY   (United States)

^b Department of Obstetrics Gynecology   (United States)

Author keywords

Critical points; Holomorphic dynamics; Lyapunov exponents

Indexed keywords

EID: 29344470767     PISSN: 10506926     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02921791     Document Type: Article

References (22)

1. 2: Currents, equilibrium measure and hyperbolicity, Invent. Math., 87, 69-99, (1990).
2. 2, III: Ergodicity, exponents and entropy of the equilibrium measure, Math. Ann., 294, 395-420, (1992).
3. 2, VI: Connectivity of J. Annals of Math., 148, 695-735, (1998).
4. 2, VII: Hyperbolicity and external rays. Annales Scientifiques de L'Ecole Normale Supérieure, to appear.
5. 2, IV: The measure of maximal entropy and laminar currents, Invent. Math., 112, 77-125, (1993).
6. 2, Invent. Math., 114, 277-288, (1993).
7. Benedicks, M. and Carleson, L. The dynamics of the Hénon map, Ann. Math., 133, 73-169, (1991).
8. Benedicks, M. and Young, L-S. Sinai-Bowen-Ruelle measures for certain Hénon maps, Invent. Math., 112, 541-576, (1993).
9. Brolin, H. Invariant sets under iteration of rational functions, Ark. Mat., 6, 103-144, (1965).
10. Chirka, E. Complex Analytic Sets, Kluwer, (1985).
11. Douady, A. and Hubbard, J.H. Itération des polynômes quadratiques complexes, C.R. Acad. Sci. Paris Série I, 294, 123-126, (1982).
12. Friedland, S. and Milnor, J. Dynamical properties of plane polynomial automorphisms, Ergodic Theory Dyn. Syst., 9, 67-99, (1989).
13. Hubbard, J.H. Hénon mappings in the complex domain, in Chaotic Dynamics and Fractals, Barnsley, M. and Demko, S., Eds., Academic Press, 101-111, (1986).
14. Hubbard, J.H. and Oberste-Vorth, R. Hénon mappings in the complex domain I: The global topology of dynamical space, Inst. Hautes Études Sci. Publ. Math., 79, 5-46, (1994).
15. Ledrappier, F. and Young, L.-S. The metric entropy of diffeomorphisms, I & II, Ann. Math., 122, 509-539 and 540-574, (1985).
16. Manning, A. The dimension of the maximal measure for a polynomial map, Ann. Math., 119, 425-430, (1984).
17. Pollicott, M. Lectures on ergodic theory and Pesin theory on compact manifolds, London Mathematical Society Lecture Note Series 180, Cambridge University Press, (1993).
18. Przytycki, F. Hausdorff dimension of harmonic measure on the boundary of an attractive basin for a holomorphic map, Invent. Math., 80, 161-179, (1985).
19. Pugh, C. and Shub, M. Ergodic attractors, Trans. AMS, 312, 1-54, (1989).
20. Sibony, N. Iteration of polynomials, U.C.L.A. Course Lecture Notes.
21. Tortrat, P. Aspects potentialistes de l'itération des polynômes, In Séminaire de Théorie du Potentiel Paris, No. 8, (Lect. Notes Math., 1235), Springer-Verlag, (1987).
22. Wu, H. Complex stable manifolds of holomorphic diffeomorphisms, Indiana U. Math. J., 42, 1349-1358, (1993).