Publications and Preprints

• Periodic orbits of non-degenerate lacunary contact forms on prequantization bundles (with Miguel Abreu). Preprint arXiv:2406.08462.

• Multiplicity, stability and symmetry of periodic orbits of Reeb flows. To appear in the proceedings of the Brazil-Portugal conference on Mathematics. Coimbra Mathematical Texts, Springer-Verlag.

• Symmetric periodic Reeb orbits on the sphere (with Miguel Abreu and Hui Liu). Trans. Amer. Math. Soc. 377 (2024), 6751-6770.

• Contact invariants of \Q-Gorenstein toric contact manifolds, the Ehrhart polynomial and Chen-Ruan cohomology (with Miguel Abreu and Miguel Moreira). Advances in Mathematics 429 (2023), Paper No. 109180.

• On contact invariants of non-simply connected Gorenstein toric contact manifolds (with Miguel Abreu and Miguel Moreira). Math. Research Letters 29 (2022), no. 1, 1-42.

• Dynamical implications of convexity beyond dynamical convexity (with Miguel Abreu). Calc. Var. Partial Differential Equations 61 (2022), no. 3, Paper No. 116, 47 pp.

• Dynamical convexity and closed orbits on symmetric spheres (with Viktor Ginzburg). Duke Math. J. 170 (2021), no. 6, 1201-1250.

• Two closed orbits for non-degenerate Reeb flows (with Miguel Abreu, Jean Gutt and Jungsoo Kang). Math. Proc. Cambridge Philos. Soc. 170 (2021), no. 3, 625-660.

• On the mean Euler characteristic of Gorenstein toric contact manifolds (with Miguel Abreu). International Mathematics Research Notices (IMRN) 2020, no. 14, 4465-4495.

• Transversality for local Morse homology with symmetries and applications (with Doris Hein and Umberto Hryniewicz). Mathematische Zeitschrift  293 (2019), no. 3-4, 1513-1599.

• Multiplicity of closed Reeb orbits on prequantization bundles (with Viktor Ginzburg and Bäsak Gurel). Israel Journal of Mathematics 228 (2018), no. 1, 407-453. 

• Dynamical convexity and elliptic periodic orbits for Reeb flows (with Miguel Abreu). Mathematische Annalen 369 (2017), no. 1-2, 331-386.

• Multiplicity of periodic orbits for dynamically convex contact forms (with Miguel Abreu). Journal of Fixed Point Theory and Applications 19 (2017), no. 1, 175-204. (Special issue "The Paul Rabinowitz Festschrift")

• Isometry-invariant geodesics and the fundamental group, II (with Marco Mazzucchelli). Advances in Mathematics 308 (2017), 671-698.

• Infinitely many periodic orbits of exact magnetic flows on surfaces for almost every subcritical energy level (with Alberto Abbondadolo, Marco Mazzucchelli and Gabriel Paternain). Journal of the European Mathematical Society 19 (2017), no. 2, 551-579.

• Brieskorn Manifolds, Positive Sasakian Geometry, and Contact Topology (with Charles Boyer and Otto van Koert). Forum Math. 28 (2016), no. 5, 943-965.

• On the existence of three closed magnetic geodesics for subcritical energies (with Alberto Abbondadolo and Gabriel Paternain). Commentarii Mathematici Helvetici 90 (2015), 155-193.

• Local contact homology and applications (with Umberto Hryniewicz). Journal of Topology and Analysis 7 (2015), 167-238.

• On the Conley Conjecture for Reeb Flows (with Viktor Ginzburg and Bäsak Gurel). Internat. J. Math. 26 (2015), 1550047 (22 pages); doi: 10.1142/S0129167X15500470.

• Closed Reeb orbits on the sphere and symplectically degenerate maxima (with Viktor Ginzburg, Doris Hein and Umberto Hryniewicz). Proceedings for the congress "Geometrical methods in Dynamics and Topology"  (celebrating the 60th anniversary of the Hanoi National University of Education) published in the special issue of the Acta Mathematica Viet. 38 (2013), 55-78.

• Remarks on Lagrangian intersections in toric manifolds (with Miguel Abreu). Transactions of the AMS 365 (2013), 3851-3875.

• Contact homology of good toric contact manifolds (with Miguel Abreu). Compositio Mathematica 148 (2012), 304-334.

• On the growth rate of leaf-wise intersections (with Will Merry and Gabriel Paternain). Journal of Symplectic Geometry {\bf 10} (2012), 601-653.

• Equivariant symplectic homology of Anosov contact structures (with Gabriel Paternain) Bulletin of the Brazilian Mathematical Society 43 (2012), 513-527.

• Positive topological entropy of Reeb flows on spherizations (with Felix Schlenk). Math. Proc. of the Cambridge Phil. Society 151 (2011), 103-128.

• On the stability of Mañé's critical hypersurfaces (with Gabriel Paternain). Calc. Var. Partial Differential Equations 39 (2010), 579-591.

• A refinement of the Hofer-Zehnder theorem on the existence of closed trajectories near a hypersurface (with Felix Schlenk). Bulletin of the London Mathematical Society 37 (2005), 297-300.

• Periodic orbits for exact magnetic flows on surfaces (with Gabriel Paternain and Gonzalo Contreras). International Mathematics Research Notices (IMRN) 8 (2004), 361-374.

• Hofer-Zehnder capacity and Hamiltonian circle actions. Communications in Contemporary Mathematics 6 (2004), 913-945.

• Entropy rigidity and harmonic fields. Nonlinearity 13 (2000), 1761-1774.

Lecture Notes

• Introduction to Symplectic Geometry (in Portuguese) (with Henrique Bursztyn). Lecture notes for a minicourse at the XIV Brazilian School of Differential Geometry, Salvador, July 2006.