Publications
Preprints
with Naiara V. de Paulo, S. Kim and A. Schneider. Transverse foliations for two-degree-of-freedom mechanical systems.
with X. Hu ; L. Liu ; Y. Ou ; G. Yu. A Symplectic Dynamics approach to the Spatial Isosceles Three-Body Problem. to appear in Journal of the European Mathematical Society.
with Naiara V. de Paulo ; S. Kim ; U. Hryniewicz. Genus zero transverse foliations for weakly convex Reeb flows on the tight 3-sphere, to appear in Advances in Mathematics.
Books
with U. Hryniewicz. Introdução à Geometria Finsler. 1. ed. Rio de Janeiro: IMPA, 2013. 208p.
with U. Hryniewicz. Uma introdução à geometria de contato e aplicações à dinâmica Hamiltoniana. 1. ed. Rio de Janeiro: IMPA, 2009. v. 1. 207p.
Published articles
with U. Hryniewicz ; K. Wysocki. Genus zero global surfaces of section for Reeb flows and a result of Birkhoff, Journal of the European Mathematical Society, 2022 (first online).
with U. Hryniewicz ; R. Siefring. Global surfaces of section with positive genus for dynamically convex Reeb flows, Journal of Fixed Points Theory and applications, first online, 2022.
with Naiara V. de Paulo. Reeb flows, pseudo-holomorphic curves and transverse foliations, Sao Paulo Journal of Mathematical Sciences, 2022.
with A. Abbondandolo ; B. Bramham ; U. Hryniewicz. Sharp systolic inequalities for Riemannian and Finsler spheres of revolution Transactions of the American Mathematical Society, 374(3), 1815-1845, 2021.
with David B. Senior ; U. Hryniewicz. On the relation between action and linking, Journal of Modern Dynamics, 17, 319-336, 2021
with A. Abbondandolo ; B. Bramham ; U. Hryniewicz. Contact forms with large systolic ratio in dimension three, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, vol. XIX (4), p 1-22, 2019.
with Naiara V. de Paulo. On the multiplicity of periodic orbits and homoclinics near critical energy levels of Hamiltonian systems in R^4, Transactions of the American Mathematical Society, v. 372 (2), p. 859-887, 2019.
with A. Abbondandolo ; B. Bramham ; U. Hryniewicz. Systolic ratio, index of closed orbits and convexity for tight contact forms on the three-sphere, Compositio Mathematica, v. 154 (12), p. 2643–2680, 2018.
with U. Hryniewicz. Global surfaces of section for Reeb flows in dimension three and beyond. Proceedings of the International Congress of Mathematicians 2018, Rio de Janeiro, Brazil.
with Naiara V. de Paulo. Systems of transversal sections near critical energy levels of Hamiltonian systems in R^4. Memoirs of the American Mathematical Society, v.252, 1202, p. 1-105, 2018.
with A. Abbondandolo ; B. Bramham ; U. Hryniewicz. Sharp systolic inequalites for Reeb flows on the three-sphere. Inventiones Mathematicae v. 211 (2), p. 687-778, 2017.
with A. Abbondandolo ; B. Bramham ; U. Hryniewicz. A systolic inequality for geodesic flows on the two-sphere. Mathematische Annalen, v. 367, p. 701-753, 2017.
with U. Hryniewicz. Elliptic bindings for dynamically convex Reeb flows on the projective three-space. Calculus of Variations and Partial Differential Equations, v. 55, p. 1-57, 2016.
with U. Hryniewicz. ; A. Momin. A Poincaré-Birkhoff theorem for tight Reeb flows on S^3. Inventiones Mathematicae, v. 199, p. 333-422, 2015.
with U. Hryniewicz ; J. Licata . A dynamical characterization of universally tight lens spaces. Proceedings of the London Mathematical Society, v. 110, p. 213-269, 2015.
with S. Addas-Zanata. Persistence of fixed points under rigid perturbations of maps. Fundamenta Mathematicae, v. 227, p. 1-14, 2014.
with U. Hryniewicz. Global properties of tight Reeb flows with applications to Finsler geodesic flows on S^2. Mathematical Proceedings of the Cambridge Philosophical Society (Print), v. 154, p. 1-27, 2013.
with J. Weber. An almost existence theorem for non-contractible periodic orbits on cotangent bundles. São Paulo Journal of Mathematical Sciences, v. 6, p. 385-394, 2013.
with W. de Melo ; E. Vargas. A full family of multimodal maps on the circle. Ergodic Theory & Dynamical Systems (Print), v. 31, p. 1325-1344, 2011.
with U. Hryniewicz. On the existence of disk-like global sections for Reeb flows on the tight 3-sphere. Duke Mathematical Journal, v. 160, p. 415-465, 2011.
with C. Grotta-Ragazzo. Global surfaces of section in non-regular convex energy levels of Hamiltonian systems. Mathematische Zeitschrift, v. 255, p. 323-334, 2007.
with M. Kulesza ; C. Grotta-Ragazzo. Equatorial dynamics of charged particles in planetary magnetospheres. Physica. D, Nonlinear Phenomena (Print), v. 225, p. 169-183, 2007.
with A. Carvalho. Assessing debt sustainability in Brazil. Brazilian Review of Econometrics, v. 27, p. 27-51, 2007.
with C. Grotta-Ragazzo. The Conley-Zehnder index and the saddle-center equilibrium. Journal of Differential Equations (Print), v. 220, p. 259-278, 2006.
The Thurston operator for semi-finite combinatorics. Discrete and Continuous Dynamical Systems, v. 16, p. 883-896, 2006.
A Conjectura de Seifert: sobre a existência de órbitas periódicas de campos de vetores em S^3. Matemática Universitária, v. 38/39, p. 69-78, 2005.
Convex energy levels of Hamiltonian systems. Qualitative Theory of Dynamical Systems, v. 4, p. 439-457, 2004.
with P. Bernard ; C. Grotta-Ragazzo. Homoclinic orbits near saddle-center fixed points of Hamiltonian systems with two degrees of freedom. Astérisque, v. 286, p. 151-165, 2003.