LIST OF PUBLICATIONS

Papers In Preparation Books


1- Structural Stability of Diffeomorphisms on two-manifolds..
Inventiones Mathematicae 21, 1973, pp.233-246
2- Stability and Optimization of Several Functions.
Topology 15, 1976, pp. 1-12
3- On the Connected Components of Morse-Smale Vector Fields on two manifolds.
Proceedings Symp. Geometry and Topology Springer Lectures Notes 597, 1977, pp. 230-251
With C. Gutierrez
4- On Linear's Equation.
Proceedings Symp. Geometry and Topology Springer Lectures Notes 597, 1977, pp. 335-357
With A.Lins Neto & C.Pugh
5- Accessibility of an Optimum.
Proceedings Symp. Geometry and Topology Springer Lecture Notes 597, 1977, pp.429-440
6- On the Structures of the Pareto Set.
Bull. of the Braz. Math. Soc. 7, no 2. 1976, pp. 121-126
7- Moduli of Stability of Two-dimensional diffeomorphisms.
Topology 19, vol. 1, 1980, pp. 9-21
8- Moduli of Stability for diffeomorphisms.
Proc. Symp. Dynamical Systems Northwestern Springer Lectures Notes 819, 1980, pp. 318-319
With J. Palis
9- Characterizing Diffeomorphisms with Modulus of Stability One.
Proc. Symp. Dynamical Systems and Turbulence - Warwick, 1980 Springer Lectures Notes 818, 1981, pp. 266-285 With J. Palis & V. Strien
10- Equivariant Diffeomorphisms with Simple Recurrence on Two-manifolds.
Trans. Amer. Math. Soc. vol. 289, n. 12, 1985, pp. 793-807
With G.L. Reis & P. Mendes.
11- A Type of Moduli for Sadle Connections of Planar Diffeomorphisms.
J. Diff. Eq., vol. 75, n. 11, 1988, pp. 88-102
With F. Dumortier
12- Diffeomorphisms on Surfaces with Finite Number of Moduli.
Ergod. Th. \& Dynam. Syst. (1987) vol. 7, pp. 415-462
With S.V. Strien
13- A Finiteness Problem for One Dimensional Maps.
Proc. AMS, 101 (4), 1987, pp. 721-727
14- One Dimensional Dynamics: The Schwarzian Derivatives and Beyond.
Bull. AMS., vol. 18, no. 2, 1988, pp. 159-162
With S.V. Strien
15- A Structure Theorem in One Dimensional Dynamics.
Annals of Mathematics, vol. 129, 1989, pp. 519-546
With S.V. Strien
16- On Cherry Flows.
Erg. Th. Dyn. Sys., vol. 10, 1990, pp. 531-554
With J. Palis & V. Strien
17- Julia-Fatou-Sullivan Theory for Real One-Dimensional Dynamics.
Acta Math., 168 (1992), 273-318
With M. Martens & S.V. Strien
18- On The C¹-Brunovske Hypothesis.
J. Diff Equations 113, n. 2, 1994, pp. 300-337
With C.C. Pugh
19- Full Families of Circle Endomorphisms.
Proc. Conf. Dynamical Systems and Chaos, Tokyo 1994,
ed. N. Aoki, K. Shiraiwa , Y. Takahashi. World Schientific, 1995, pp. 25-27.
20- The Cost of Computing Integers.
Proc. Am. Math. Soc. vol. 124, no. 5, 1996, pp. 1377-1378
With B.F. Svaiter
21- On the Cyclicity of Recurrent Flows on Surfaces.
Nonlinearity, 10 (1997) no. 2, 311--319
22- Universal Models for Lorenz Maps.
With M. Martens
Preprint IMPA.
SUNY StonyBrook Preprint 1996/12
Erg.Th. and Dyn. Sys. 21 (2000) bo.2, 343--370
23- Rigidity of critical circle mappings I
J.Eur.Math.Soc., 1, 1999, no 4, 339--392
With E. de Faria
24- Rigidity of critical circle mappings II
With E. de Faria
J.Am.Math. Soc. 13., no. 2., 2000, 343--370
25- The Multipliers of Periodic Point in One-Dimensional Dynamics
With M. Martens
Nonlinearity 12 ( 1999) no. 2, 217---227
26- Rigidity and Renormalization in One Dimensional Dynamical Systems
Proc. Int. Congr. Mathematicians, Berlim, 1998,
Documenta Mathematica, Extra Volume ICM 98, Vol. II 765--778
Preprint IMPA.
27- Rigidity of C2 infinitely renormalizable unimodal maps
Comm. Math. Phys. 208 (1999) 91--105
With A. A. Pinto
28- On the Dynamics of the Renormalization Operator
( postcript) Preprint IMPA.
With A. Avila and M. Martens
Global Analysis on Dynamical Systems, pp. 449--460
Ed. H. Broer, B. Krauskopf, G. Vegter
IOP Publishing Ltd. (2001)
30- Regular or stochastic dynamics in real analytic families of unimodal maps
With A. Avila and M. Lyubich
Inventiones Mathematicae, n.3, v. 154, 2003, 451--550
PS file (final version) IMPA.
29- Global Hyperbolicity of Renormalization for $C^r$ Unimodal Mappings
With E. de Faria and A. A. Pinto
(gzipped postscript)

Back to top.

IN PREPARATION


Back to top.

BOOKS

1- Introdução aos Sistemas Dinâmicos.
Edgar Blucher,
With J. Palis
2- Geometric Theory of Dynamical Systems.
Springer-Verlag, 1980.
With J.Palis
3- Lectures on One-Dimensional Dynamics.
Publ. do 17º Colóquio Brasileiro de Matemática, 1988
4- One Dimensional Dynamics.
Springer-Verlag, 1993
With S. Van Strien
5- One-dimensional dynamics. The mathematical tools.
IMPA's Mathematical Publications, 23rd Brazilian Mathematics Colloquium, Instituto de Matematica Pura e Aplicada (IMPA), (2001)
With E. de Faria

Back to home page





Last Update: Mar. 1996
Edit by: Gilza & Rachel