Research Interests (MSC2010):

Dynamical Systems and Ergodic Theory (in particular One-dimensional Dynamics and Renormalization)
Conformal Geometry and Teichmüller Theory
Quantum Physics

Work in Progress

Growth, entropy-type invariants and regularity (Parts I and II) (with Peter Hazard and Charles Tresser), in preparation

Preprints (see also arXiv)


Asymptotically holomorphic methods for infinitely renormalizable Cr unimodal maps (with Trevor Clark and Sebastian van Strien)
To appear in Ergodic Theory and Dynamical Systems
arXiv preprint https://arxiv.org/abs/1804.06122

Quasisymmetric orbit-flexibility of multicritical circle maps (with Pablo Guarino)
To appear in Ergodic Theory and Dynamical Systems
arXiv preprint https://arxiv.org/abs/1911.04375

Published Articles

Dynamics of multicritical circle maps (with Pablo Guarino)
São Paulo Journal of Mathematical Sciences 16 (2022), 340--395.
DOI Number:10.1007/s40863-021-00236-1.

There are no σ-finite invariant measures for multicritical circle maps (with Pablo Guarino)
Nonlinearity 34 (2021), 6727--6749.
DOI Number:10.1088/1361-6544/ac1a02.

Genericity of infinite entropy for maps with low regularity (with Peter Hazard and Charles Tresser)
Annali della Scuola Normale Superiore di Pisa Cl. Sci. (5) XXII (2021), 601--664.
DOI Number: 10.2422/2036-2145.201807_004.

On the Erdős-Sloane and shifted Sloane persistence problems (with Gabriel Bonuccelli and Lucas Colucci)
Journal of Integer Sequences 23 (2020), Article 20.10.7.

Generalized Whitney topologies are Baire (with Peter Hazard).
Proceedings of the American Mathematical Society 148 (2020), 5441--5455.

On slow growth and entropy-type invariants (with Peter Hazard and Charles Tresser)
New Trends in One-dimensional Dynamics, Springer Proceedings in Mathematics & Statistics, 285 (2019), 165--181, (P. Guarino and M.J. Pacifico, eds.), Springer Verlag.

Real bounds and quasisymmetric rigidity of multicritical cicle maps (with Gabriela Estevez)
Transactions of the American Mathematical Society 370 (2018), 5583--5616.

Beau bounds for multicritical circle maps (with Gabriela Estevez and Pablo Guarino)
Indagationes Mathematicae 29 (2018), 842--859.

Infinite entropy is generic in Holder and Sobolev Spaces (with Peter Hazard and Charles Tresser)
Comptes Rendus de l'Academie des Sciences de Paris Ser. I 355 (2017), 1185--1189.

Real bounds and Lyapunov exponents (with Pablo Guarino)
Discrete and Continuous Dynamical Systems 36 (2016), 1957--1982.

Differentiability of correlations in realistic quantum mechanics (with Alejandro Cabrera, Enrique Pujals, Charles Tresser)
Journal of Mathematical Physics 56 (2015), 092104.

On Sloane's persistence problem (with Charles Tresser)
Experimental Mathematics 23 (2014), 363--382.

Bell inequality violations under reasonable and under weak hypotheses (with Charles Tresser)
Physical Review Letters 110 (2013), 260409.

David homeomorphisms via Carleson boxes
Annales Academiae Scientiarum Fennicae Mathematica 36 (2011), 215--229.

Thompson's group, Teichmüller spaces, and dual Riemann surfaces,
Dynamics, Games and Science, Springer Proceedings in Mathematics 1 (2011), 323--338.
Conference DYNA2008 in honour of Mauricio Peixoto and David Rand, September 8-12, 2008,
Universidade do Minho, Braga, Portugal. Ed. by M. Peixoto, D. Rand, A. Pinto. Springer-Verlag.

An introduction to the thermodynamics of conformal repellers
São Paulo Journal of Mathematical Sciences 4 (2010), 65--91.

Global hyperbolicity of renormalization for Cr unimodal maps (with Welington de Melo and Alberto Pinto),
Annals of Mathematics 164 (2006), 724--831.

Thompson's group as a Teichmüller mapping class group (with Frederick Gardiner and William Harvey),
Contemporary Mathematics 355 (2004), 165--185.

Aspects of rigidity and universality in one-dimensional dynamics
Fields Institute Communications 31 (2002), 113--123.

Rigidity of critical circle mappings II (with Welington de Melo),
Journal of the American Mathematical Society 13 (2000), 343--370.

Rigidity of critical circle mappings I (with Welington de Melo),
Journal of the European Mathematical Society 1 (1999), 339--392.

Asymptotic rigidity of scaling ratios for critical circle mappings
Ergodic Theory and Dynamical Systems 19 (1999), 995--1035.

On conformal distortion and Sullivan's sector theorem
Proceedings of the American Mathematical Society 126 (1998), 67--74.

Quasisymmetric distortion and rigidity of expanding endomorphisms of S1
Proceedings of the American Mathematical Society 124 (1996), 1949--1956.

Limit laws of entrance times for homeomorphisms of the circle (with Zaqueu Coelho),
Israel Journal of Mathematics 93 (1996), 93--112.

A-priori bounds for C2 homeomorphisms of the circle
Resenhas do IME-USP 1, 4 (1995), 487--493.

Books

Mathematical Aspects of Quantum Field Theory (with Welington de Melo)
Cambridge Studies in Advanced Mathematics 127 (2010), Cambridge University Press.

Mathematical Tools for One-dimensional Dynamics (with Welington de Melo)
Cambridge Studies in Advanced Mathematics 115 (2008), Cambridge University Press.

Dynamics of Circle Mappings (with Pablo Guarino)
33º Colóquio Brasileiro de Matemática, IMPA Mathematical Publications (2021).

Expository Work

Period doubling bifurcations (with Pierre Coullet and Charles Tresser),
Scholarpedia 9(6), 3958 (2014) .

Welington de Melo (1946--2016) (with Sebastian van Strien),
New Trends in One-dimensional Dynamics, Springer Proceedings in Mathematics & Statistics, 285 (2019), 7--20, (P. Guarino and M.J. Pacifico, eds.), Springer Verlag.

Colloquium Lectures

Dynamics of Circle Mappings(with Pablo Guarino),
33º Colóquio Brasileiro de Matemática, IMPA Mathematical Publications (2021).

Mathematical Aspects of Quantum Field Theory (with Welington de Melo),
26º Colóquio Brasileiro de Matemática, IMPA Mathematical Publications (2007).

One-dimensional dynamics: the mathematical tools(with Welington de Melo),
23º Colóquio Brasileiro de Matemática, IMPA Mathematical Publications (2001).