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o     Pontos Umbílicos em Leis de Conservação, Master’s Thesis, University of Porto, 2001.

o     Analytic Classification of Complex Differential Equations, Ph.D. Thesis, University of Porto, 2006

o     The geometry and dynamics of complex ordinary differential equations, Habilitation, University of Porto, 2021





Published Papers and Preprints


[17]        (with A. Belotto, M. Klimes, J.C. Rebelo) Liouvillian integrability of vector fields and meromorphic solutions, preprint

[16]        (with A. Belotto, M. Klimes, J.C. Rebelo) A remark on first integrals of vector fields, submitted

[15]        (with J.C. Rebelo) On resolution of 1-dimensional foliations on 3-manifolds,

Russian Mathematical Surveys, Vol. 76, nº 2 (2021), 291-355

Translated to Russian and published in: Uspekhi Mat. Nauk, Vol. 76, no 2 (458), 103-176 (2021)

(arXiv version)

[14]        (with A.C. Ferreira, J.C. Rebelo) Palais leaf-space manifolds and surfaces carrying holomorphic flows

Moscow Mathematical Journal, vol. 19, nº 2 (2019), 275-305

(arXiv version).

[13]        (with J.C. Rebelo) Discrete orbits, recurrence and solvable subgroups of Diff(C2,0)

Journal of Geometric Analysis, vol. 27, nº 1 (2017), 1-55

(arXiv version)

(previous versions).

[12]        (with J.C. Rebelo) 2-dimensional Lie algebras and separatrices for vector fields on (C3,0)

Journal de Mathématiques Pures et Appliquées, vol. 105, nº 2 (2016), 248-264

(arXiv version).

[11]        (with J.C. Rebelo) A note on integrability and finite orbits for subgroups of Diff(Cn,0)

Bulletin Brazilian Math. Soc., vol. 46, nº 3 (2015), 469-490

(arXiv version).

[10]        (with J.C. Rebelo) Uniformizing complex ODE'S and applications

              Revista Matemática Iberoamericana, vol. 30, nº 3 (2014), 799–874

              (arXiv version)

[9]         (with S. Pinheiro) Topological aspects of completely integrable foliations

              Journal London Math. Soc. (2), vol. 89, nº 2 (2014), 415–433

              (arXiv version)

[8]         (with J.C. Rebelo) Cyclic stabilizers and infinitely many hyperbolic orbits for pseudogroups on (C,0)

Journal of the Institute of Mathematics of Jussieu, vol. 13, nº 2 (2014), 413-446.

(arXiv version)

[7]         (with J.F. Mattei, J.C. Rebelo) Generic pseudogroups on (C,0) and the topology of leaves

Compositio Mathematica, vol. 149, nº 8 (2013), 1401 - 1430.

(arXiv version)

[6]         (with J.C. Rebelo) Separatrices for C2-actions on 3-manifolds

Commentarii Mathematici Helvetici, vol. 88, nº 3 (2013), 677–714.

[5]         Semi-complete vector fields of saddle-node type in Cn

Transactions of the AMS, vol. 360, nº 12 (2008), 6611-6630.

[4]         Semi-complete foliations associated to Hamiltonian vector fields in dimension 2

J. Math. Anal. Appl.,vol. 328, nº 2 (2007), 813-820.

[3]         Equivalence and semi-completude of foliations

Nonlinear Analysis. Theory, Methods and Applications, vol. 64, nº8 (2006), 1647-1896.

[2]         (with J.B. Gonçalves) The geometry of quadratic 2×2 systems of conservation laws

Acta Appl. Math., vol. 88, nº 3 (2005), 269 – 329.

[1]          (with J.B. Gonçalves) The geometry of conservation laws

The J. A. Pereira da Silva Birthday Schrift – Textos de Matemática (série B), nº 32, Departamento da Matemática FCTUC (2002), 17-33.





Papers in Preparation


o   (with A. Belotto, M. Klimes, J. Rebelo) Dynamics of Airy equation, P-I and P-II

o   (with A. Elshafei, A.C. Ferreira) Geodesic completeness of Pseudo-Riemannian metrics in Lie groups.

o   (with A. Elshafei, J. Rebelo) Meromorphic vector fields and PSL(2,C)






Other Manuscripts


o   (with A.C. Ferreira, J.C. Rebelo) Complete commuting vector fields and their singular points in dimension 2 (available from arXiv: 1809.09255)

o   (with J.C. Rebelo) Local Theory of Holomorphic Foliations and Vector Fields (Lecture Notes of an advanced course available from arXiv:1101.4309)

o   (with J.C. Rebelo) Dynamics and Geometry on Homogeneous Spaces: An Introduction (Lecture Notes of an advanced course)





(Last update: July 2021)


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