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Mildly dissipative diffeomorphisms of the disk with zero entropy, Acta Mathematica, Volume 232 (2024) Number 2, 221-323 (with Sylvain Crovisier and Charles Tresser)
Robust transitivity and domination for endomorphisms displaying critical points, Ergodic Theory and Dynamical
Systems, Volume 44 , Issue 2 , February 2024 , pp. 594 - 629 (with C. Lizana, R. Potrie and W. Ranter).
From zero to positive entropy, Notices Amer. Math. Soc. 69 (2022), no. 5, 748–761 (with Sylvain Crovisier).
Germ-typicality of the coexistence of infinitely many sinks, Adv. Math. 407 (2022), Paper No. 108528, 51 pp (with Pierre Berger and Sylvain Crovisier)
Orders of Growth and Generalized Entropy, J. Inst. Math. Jussieu 22 (2023), no. 4, 1581–1613. (with Javier Correa)
Dynamics of generalized hyperbolic linear operators, Adv. Math. 387 (2021), (with Patricia Cirilo and Bryce Gollobit)
Invariance of entropy for maps isotopic to Anosov, Nonlinearity 34 (2021), no. 3, 1612–1632. (with Pablo Carrasco, Cristina Lizana and Carlos Vasquez)
Classification of partially hyperbolic diffeomorphisms under some rigid conditions, Erg. Th. and Dyn. Sys 41 (2021) 2770–2781. (with Pablo Carrasco and Federico Rodriguez Hertz)
Stable and non-symmetric pitchfork bifurcations, Sci. China Math. 63 (2020), no. 9, 1837–1852, (with Mike Shub and Yun Yang)
Linear independence of time-frequency translates in Lp spaces, J. Fourier Anal. Appl. 26 (2020), no. 4, Paper No. 63, 15 pp., (with Jorge Antezana and Joaquim Bruna).
Discrete dynamics and stacks, Rev. Mat. Iberoam. 36 (2020), no. 7, 2121–2146, (with Alejandro Cabrera and Matias del Hoyo)
A divergence theorem for non-compact Riemannian manifolds: A dynamical approach, Nonlinearity (2019), volume 32, issue 3, (with Italo Melo).
Strongly dissipative diffeomorphisms, Commentarii Mathematici Helvetici (2018), volume 93, issue 2, 377-400
(with S. Crovisier).
Expansivity and Shadowing in Linear Dynamics, Journal of Mathematical Analysis
and Applications 461, (2018), 796-816 (with N. Bernardes, P. Cirilo, U. Darji, A. Messaoudi).
Holder stability for C^r-central translations, in Mathematische Zeitschrift 286 (2017),no. 1-2,121139 (with Javier Correa).
Desingularization of surface maps, Electronic Research Announcements in Mathematical Sciences
Volume 24, Pages 19 (2017) (with E. Clay and B. Hasselblatt).
Iterated Function, Blenders and Parablenders, Recent Developments in Fractals and Related Fields:
Conference on Fractals and Related Fields III, ˆıle de Porquerolles ISBN 978-3-319-57805-7, (2017),
57-70, (with P. Berger , S. Crovisier).
Ergodic properties of skew products in infinite measure, Israel Journal of Mathematics 214 (2016),
43-66, (with P. Cirilo, Y. Lima).
Inventiones Mathematicae, (2015) Volume 201, Issue 2, 385-517 (with S. Crovisier).
Differentiability of correlations in realistic quantum mechanics, J. Math. Phys. 56, 092104 (2015)
(with Alejandro Cabrera, Edson de Faria, Charles Tresser).
Partially hyperbolic geodesic flows, Annales de l’Institut Henri Poincare (C) Non Linear Analysis
(5), (2014), 985-1014 (with F. Carneiro).
Some Consequences of the Shadowing Property in Low Dimensions, Ergodic Theory and Dynamical
Systems (4), (2014), 1273-1309 (with A. Koropecki).
Law of large numbers for certain cylinder flows, Ergodic Theory and Dynamical Systems (4),
(2014), 801-825 (with P. Cirilo, Y. Lima).
Axiom A versus Newhouse phenomena for Benedicks-Carleson toy models, Annales scientifiques de
l’Ecole Normale Sup ́erieur (46), fascicule 6, (2013), 857-878, (with C. Matheus and C.G. Moreira).
Robust transivity for Endomorphisms, Ergodic Theory and Dynamical Systems (33), 04, (2013),
1082-1114 (with C. Lizana).
Patterns of Attractors in the ”Brain”. Wild Dynamics at the Edge, SmartData Privacy Meets
Evolutionary Robotics Springer Verlag, ISBN 978-1-4614-6408-2, (2013), 91-106.
Robust transivity in Hamiltonian Dynamics, Annales scientifiques de l’Ecole Normale Sup ́erieur
(45), fascicule 2 (2012), 191-239, (with M. Nassiri).
The iterated Aluthge transforms of a matrix converge, Advances in Mathematics (226), (2011),
1591-1620 (with J. Antezana and D. Stojanoff).
Infinite ergodic theory and Non-extensive entropies. Brazilian Journal of Physics Volume 41,
Numbers 4-6 (2011), 297-303, (with L.M. Gaggero-Sager, O. Sotolongo-Costa)
Self-Similarity in Semiconductors: Electronic and Optical Properties, Optoelectronics - Materials
and Techniques,ISBN 978-953-307-276-0,(2011), 435-458, (with L.M. Gaggero-Sager, D. S. Diaz-
Guerrero and J. Escorcia-Garc ́ıa).
Two-dimensional Blaschke products: degree growth and ergodic consequences, Indiana University
Mathematics Journal (59) (2010), 301-326, (with R. Roeder).
Pinball billiards with dominated splitting, Ergodic Theory and Dynamical Systems (30), (2010)
1757-1786, (with R. Markarian and M. Sambarino).
On the dynamics of dominated splitting, Annals of Mathematics (169) (2009), 675-740 (with M.
Sambarino)
From Peixoto’s theorem to Palis’s conjecture, Dynamics, Games and Science I DYNA 2008, in
Honor of Maurcio Peixoto and David Rand (2008) Springer Proceedings in Mathematics, Vol. 1.
Density of hyperbolicity and tangencies in sectional dissipative regions, in Annales de l’Institut
Henri Poincare (C) Non Linear Analysis, Volume 26, Issue 5, (2009), Pages 1971-2000 (with M.
Singular-hyperbolic attractors are chaotic, in Transactions of the American Mathematical Society
(361) (2009), 2431-2485. (with V. Araujo; M. Pacifico; M.Viana)
Convergence of iterated Aluthge transform sequence for diagonalizable matrices II: λ-Aluthge
transform, in Integral Equations and Operator Theory vol. 62, no. 4, (2008), pp. 465-488 (with J.
Antezana and D. Stojanoff).
Some simple questions related to the C^r-stability conjecture, Nonlinearity (21) (2008) 233-237.
Trying to characterize robust and generic dynamics, New Trends in Mathematical Physics Selected
contributions of the XVth International Congress on Mathematical Physics 978-90-481-2810-5,
2009, Springer.
Dynamics of two dimensional Blaschke products, Ergodic Theory and Dynamical Systems, Volume
28, Issue 02, April 2008, pp 575-585 (with M. Shub).
A continous Bowen-Mane type phenomenon, Discrete and Continuous Dynamical System 20
(2008), no. 3, 713–724, (with E. Mu ̃noz Young; A Navas; C. Vasquez)
Covergences of iterated Aluthge transform sequence for diagonalizable matrices Advances in Math-
ematics Volume 216, September 2007, Pages: 255-278 (with J. Antezana and D. Stojanoff).
Critical points for surfaces maps, Journal of Modern Dynamics Volume 1, No. 4, 2007 (with F.
Rodriguez Hertz).
From hyperbolicity to dominated splitting, Proceedings of the Partially hyperbolic dynamics, lam-
inations, and Teichmuller flow Workshop, 89–102, Fields Inst. Commun., 51, Amer. Math. Soc.,
Providence, RI, 2007.
Vortex dynamics and their interactions in quantum trajectories, Journal of Physics A: Mathemat-
ical and Theoretical volume: 40, 2007, pages: 1–16 (with F. Borondo and D. A. Wisniacki).
Dynamical properties of singular hyperbolic attractors, Discrete and Continuous Dynamical Sys-
tem Volume 19, Number: 1 , September 2007, Pages: 67 – 87 (with A. Arroyo).
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.
Integrability on codimension one dominated splitting, Bulletin of the Brazilian Mathematical So-
ciety, New Series 38 (2007), no. 1, 1–19. (with M. Sambarino).
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).
Heterodimensional tangencies, Nonlinearity 19 No 11 (November 2006) 2543-2566(with Lorenzo
J. D ́ıaz, Adriana Nogueira).
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.
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).
A sufficient conditions for robustly minimal foliations, Ergodic theory and dynamical systems Vol-
ume 26, Issue 01, Feb 2006, pp 281-289 (with M. Sambarino).
Topics on homoclinic bifurcation, dominated splitting, robust transitivity and related results,
Handbook of dynamical systems vol 1B, Elsevier (2005) 327-378 (with M. Sambarino).
Vortices, complexity and probabilities in the quantum fluid, Europhys. Lett, 73 (5), pp. 671-676
(2006) (with F. Borondo and D. A. Wisniacki).
Motion of vortices implies chaos in Bohmian mechanics, Europhys. Lett., 71 (2), pp. 159-165
(2005) (with D. A. Wisniacki).
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).
Robust expansive homoclinic classes, Ergodic Theory and Dynamical Systems (2005), 25: 271-300
(with M.J. Pac ́ıfico and J. Vieitez)
Intransitivity Revisited: Coevolutionary Dynamics of Numbers Games, Genetic and Evolutionary
Computation Conference (GECCO-2005) (with P. Funes).
Robust transitive singular sets for 3-flows are partially hyperbolic attractors or repellers, Annals
of Mathematics, 160, no 2, (2004), 375-432 (with C. A. Morales and M.J. Pacifico).
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).
Robustly transitive sets and heterodimensional cycles. Geometric methods in dynamics. I. Aster-
isque No. 286 (2003), xix, 187–222 (with C. Bonatti, L. Diaz and J. Rocha).
Tangent bundles dynamics and its consequences. Proceedings of the International Congress of
Mathematicians, Vol. III (2002), 327–338, Higher Ed. Press, Beijing, 2002.
Homoclinic tangencies and hyperbolicity for surface diffeomorphisms, Annals of Mathematics, 151
(2000), 961-1023 (with M. Sambarino).
Self-similarity in a Cantor like semiconductor quantum well. Physica status solidi B , 220, 167
(2000) (with L.M. Gaggero-Sager and O. Sotolongo).
Strange attractors across the boundary of hyperbolic systems, Comm. Math. Phys. 211 (2000)
527-558 (with C. A. Morales and M. J. Pac ́ıfico).
On homoclinic tangencies, hyperbolicity, existence of homoclinic orbits and variation of entropy,
Nonlinearity 13 (2000), no. 3, 921-926 (with M. Sambarino).
Partial hyperbolicity and robust transitivity, Acta Mathematica 183, no. 1 (1999), 1-43 (with L.J.
Diaz and R. Ures).
Singular hyperbolic sets, Procs. A. M. S. 127 (1999) 3393–3401, (with C. A. Morales and M.J.
Pacıfico).
Strange attractors containing a singularity with two positive multipliers, Comm. Math. Phys. 196
(1998), 671–679 (with C. A. Morales).
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. Pacıfico).
Global attractors from the explosion of singular cycles, Comptes Rendus de l’Acad. des Sciences
de Paris 325 (1997), 1317–1322 (with C. A. Morales and M. J. Pacıfico).
Singular strange atractors on the boundary of Morse-Smale systems, Annales Scient. Ecole Nor- ́
male Superieure 30 (1997), 693-717 (with C. A. Morales).
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