List of Publications.

I- Published and accepted for publication (organized by year of publication).

  1. Two-dimensional Blaschke products: degree growth and ergodic consequences, to appear in Indiana University Mathematics Journal (with R. Roeder)

  2.  Pinball billiards with dominated splitting , to appear in Ergodic Theory and Dynamical Systems,  (with R. Markarian and R.  Sambarino).

  3. On the dynamics of dominated splitting, Annals of Mathematics (169) (2009), 675-740 (with M. Sambarino)

  4. Density of hyperbolicity and tangencies in sectional dissipative regions, in  Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Volume 26, Issue 5, September-October 2009, Pages 1971-200 (with  M. Sambarino).

  5. Singular-hyperbolic attractors are chaotic, in Transactions of the  American Mathematical Society (361)  (2009), 2431-2485. (with V. Araujo;  M. Pacifico;  M. Viana)  

  6. Convergence of iterated Aluthge transform sequence for diagonalizable matrices II: $\lambda$-Aluthge transform,  in Integral Equationsand Operator Theory  vol. 62, no. 4, (2008), pp. 465-488 (with J. Antezana and D. Stojanoff).

  7. Some simple questions related to the $C^r$ stability conjecture, Nonlinearity (21) (2008)  233-237.

  8. Trying to characterize robust and generic dynamics, New Trends in Mathematical Physics Selected contributions of the XVth International Congress on Mathematical Physics  Springer.

  9.  Dynamics of two dimensional Blaschke products,  Ergodic

  10. Theory and Dynamical Systems,  Volume 28, Issue 02, April 2008, pp 575-585 (with  M. Shub).

  11. A non-hyperbolic Bowen-Mane type phenomenon,   Discrete and Continuous Dynamical System  20  (2008),  no. 3, 713--724, (with E. Munoz Young; A Navas; C. Vasquez) 

  12. Covergences of iterated Aluthge transform sequence for diagonalizable matrices  Advances in Mathematics Volume 216, September 2007, Pages: 255-278 (with J. Antezana and D. Stojanoff).

  13. Critical points for surfaces maps, {\em Journal of Modern Dynamics Volume 1, No. 4, 2007  (with F. Rodriguez Hertz).

  14. From hyperbolicity to dominated splitting,  Proceedings of the Partially hyperbolic dynamics, laminations, and Teichmuller flow Workshop, 89--102, Fields Inst. Commun., 51, Amer. Math. Soc., Providence, RI, 2007.

  15. Vortex dynamics and their interactions in quantum trajectories Journal of  Physics A: Mathematical and Theoretical volume: 40, 2007, pages: 1--16 (with F. Borondo and D. A Wisniacki).

  16. Dynamical properties of singular hyperbolic attractors, Discrete and Continuous Dynamical System Volume 19, Number: 1 , September 2007, Pages:  67  --  87 (with A. Arroyo).

  17. Density of hyperbolicity and homoclinic bifurcations for topologically hyperbolic sets, in Discrete and Continuous Dynamical System, Vol 20, n 2, February 2008, pp 337--408.

  18. Integrability on codimension one dominated splitting, Bulletin of the Brazilian Mathematical Society, New Series   38  (2007),  no. 1, 1--19. (with M. Sambarino). 

  19. Expanding maps of the circle rerevisited: Positive Lyapunov exponents in a rich family, Ergodic Theory and Dynamical Systems,  Volume 26,  Issue 06, Dec 2006, pp 1931-1937 (with L.  Robert and M. Shub).

  20. Heterodimensional tangencies, Nonlinearity 19 No 11 (November 2006) 2543-2566(with Lorenzo J. Diaz, Adriana Nogueira).

  21. On the density of hyperbolicity and homoclinic bifurcations for 3D diffeomorphism in attracting regions,  Discrete and Continuous Dynamical System Volume 16, Number: 1 , September 2006. Pages:  179  --  226

  22. Non-huniform hyperbolicity for stable ergodic maps, Comptes Rendus de l'Acad des Sciences de Paris  Ser. I 342 (2006), 763-766. (with B. Fayad and J. Bochi).

  23. A sufficient conditions for robustly minimal foliations,  Ergodic theory and dynamical systems    Volume 26,  Issue 01, Feb 2006, pp 281-289 (with M. Sambarino).

  24. Topics on homoclinic bifurcation, dominated splitting,  robust transitivity and related results, Handbook  of dynamical systems vol 1B, Elsevier (2005) 327-378 (with M. Sambarino).

  25.  Vortices, complexity and probabilities in the quantum fluid, Europhys. Lett, 73 (5), pp. 671-676 (2006)  (with F. Borondo and D. A. Wisniacki).

  26. Motion of vortices implies chaos in Bohmian mechanics, Europhys. Lett., 71 (2), pp. 159-165 (2005)  (with D. A. Wisniacki).

  27. Dynamical zeta functions for analytic surface diffeomorphisms with dominated splitting, Journal of the Institute of Mathematics of Jussieu,  Volume 4, Issue 02, (2005), pp 175-218 (with V. Baladi and M. Sambarino).

  28. Robust expansive homoclinic classes, Ergodic Theory and Dynamical Systems  (2005), 25: 271-300 (with M.J. Pacifico and J. Vieitez)

  29. Intransitivity Revisited: Coevolutionary Dynamics of Numbers Games, Genetic and Evolutionary Computation Conference (GECCO-2005)  (with P. Funes).

  30. Robust transitive singular sets for $3$-flows are partially hyperbolic attractors or repellers, Annals of Mathematics, 160, no 2, (2004), 375-43  (with C. A. Morales and M.J. Pacifico).

  31. A $C^1$ generic dichotomy for diffeomorphisms: weak forms of hyperbolicity or infinitely many sinks or sources,  Annals of Mathematics, 158 (2003), 355-418 (with C. Bonatti, and L.J. Diaz).

  32. Robustly transitive sets and heterodimensional cycles  Geometric methods in dynamics. I.  Asterisque  No. 286 (2003), xix, 187--222 (with C. Bonatti, L. Diaz and J. Rocha).

  33. Tangent bundles dynamics and its consequences. Proceedings of the International Congress of Mathematicians, Vol. III (2002), 327--338, Higher Ed. Press, Beijing, 2002.

  34. Homoclinic tangencies and hyperbolicity for surface diffeomorphisms, Annals of Mathematics, 151 (2000), 961-1023 (with M. Sambarino).

  35.  Self-similarity in a Cantor like semiconductor quantum well. Physica status solidi B , 220, 167 (2000) (with L.M. Gaggero-Sager and O. Sotolongo).

  36. Strange attractors across the boundary of hyperbolic systems, Comm. Math. Phys. 211 (2000) 527-558  (with C. A. Morales and M. J. Pacifico).

  37. On homoclinic tangencies, hyperbolicity, existence of homoclinic orbits and variation of entropy, Nonlinearity 13 (2000), no. 3, 921-926 (with M. Sambarino).

  38. Partial hyperbolicity and robust transitivity,  Acta Mathematica 183, no. 1 (1999), 1-43 (with L.J. Diaz and R. Ures).

  39. Singular hyperbolic sets,  Procs. A. M. S. 127 (1999) 3393--3401, (with C. A. Morales and M.J. Pacifico).

  40. Strange attractors containing a singularity with two positive multipliers, Comm. Math. Phys. 196 (1998), 671--679 (with C. A. Morales).

  41. On $C^1$-robust singular transitive sets for three dimensional flows, Comptes Rendus de l'Acad des Sciences de Paris 326 (1998), 81--86 (with C. A. Morales and M. J. Pacifico). Comptes Rendus de l'Acad. des Sciences de Paris 325 (1997), 1317--1322 (with C. A. Morales and M. J. Pacifico). Global attractors from the explosion of singular cycles,

  42.  Singular strange atractors on the boundary of Morse-Smale systems, Annales Scient. \'Ecole Normale Sup\'erieure 30 (1997), 693--717 (with C. A. Morales).

II- Submited and preprint

some available at http://www.preprint.impa.br/cgi-bin/MMMsearch.cgi

  1. Wave functions in a topologically self-similar quantum well (with L.M. Gaggero Sager)

  2. Saddle-node focus singular cycles.

  3.   Contracting Lorenz attractors through singular cycles.

  4. The iterated Aluthge transforms of a matrix converge (with J. Antezana and D. Stojanoff)

  5. Robust transivity in Hamiltonian Dynamics (with M. Nassiri)

III-  In preparation.

  1. On $C^1-$density of hyperbolicity for two dimensional maps (with Carlos Matheus, Carlos G. Moreira)

  2.  Structural stability for diffeomorphisms on surfaces with boundary, (with A. Arroyo).

  3. Melnikov methods for partially hyperbolic sytems, (with A. Wilkinson, C. Pugh and M. Shub).

  4. Super exponential growth of periodic points in heteroclinic cycles, (with V. Kaloshin).

  5.  Partial hiperbolic system and N-central forces in celestial mechanics, (with L. Florit and V. Kaloshin).

  6.  Hyberbolicity and heterodimensional cycles for partially  hyperbolic skew products, (with S. Crovissier).

  7. Hyberbolicity versus homoclinic bifurcations, (with S. Crovissier).

  8. Equilibrium Selection in Infinitely Repeated Games, (with P. Dal Bo).