Personal Data

Full name

Pedro Miguel Nunes da Rosa Dias Duarte

Publishing name

Pedro Miguel Nunes da Rosa Dias Duarte

Birthday

1962-03-02T00:00:00

Academic Degrees

LICENCIATURA(0)

Degree date

1985

Final grade

Dezanove valores

Degree granting institution

Universidade de Lisboa

School / College / Campus

Faculdade de Ciências

Thesis title

Uma discreta abordagem à geometria

Supervisor

Armando Henrique Prazeres Machado

Co-supervisor

-

Scientific area

Matemtática

DOUTORAMENTO(0)

Degree date

1993

Final grade

n/a

Degree granting institution

Outra

School / College / Campus

Other

Thesis title

Plenty of elliptic islands for the standard family of area preserving maps

Supervisor

Jacob Palis

Co-supervisor

-

Scientific area

Sistemas Dinâmicos

AGREGAÇÃO(0)

Degree date

2017

Final grade

n/a

Degree granting institution

Universidade de Lisboa

School / College / Campus

Faculdade de Ciências

Thesis title

Dinâmica Caótica e Regular

Supervisor

n/a

Co-supervisor

n/a

Scientific area

Matemática

Profissional activity

Period Position Institution
from October 2000 until now Assistant Professor Faculdade de Ciências de Lisboa
from November 1995 to October 2000 Assistant Professor Instituto Superior Técnico
from May 1993 to November 1995 Assistant Professor Faculdade de Ciências de Lisboa
from October 1985 to May 1993 Assistant Faculdade de Ciências de Lisboa

Area of scientific activity

Area of scientific activity

Mathematics

Specialization domain

Dynamical Systems

Current main scientific area

Discrete Dynamical Systems: Conservative and symplectic dynamics, evolutionary game dynamics, random dynamical systems, billiard maps, linear cocycles.

Other scientific activities

Use of informatic technologies in the teaching/assessment/learning process.

Experience as scientific advisor

Maria João Quintão Pereira (Undergraduate Dissertation), October (2001), IST-UTL
Pedro Pantoja, (Tutoria Novos Talentos) (2010-2011) FCUL
Paulo Coelho (MSc), December, (2008) FCUL
Telmo Peixe (MSc), December, (2010) FCUL
João Carmona, (MSc), October, (2012) FCUL
Pedro Pinto (MSc co-supervision) , December, (2013) FCUL
Maria Joana Torres (PhD), July, (2004) FCUL
Telmo Peixe (PhD), November (2015) FCUL
Nuno Matos Luzia (Postdoc) (2008-2009) FCUL
Silvius Klein (Postdoc) (2013) FCUL
Mohammad Soufi (Postdoc) (2013) FCUL
Hassan Alishah (Postdoc) (2013) FCUL
Manuel Santos, (Tutoria Novos Talentos) (2015-2016) FCUL

Participations in R&D projects

Geometric and Topological Methods in Hamiltonian Dynamical Systems and Ergodic Theory, FCT, PBIC/C/MAT/2140/95

Variedades diferenciáveis combinatóricas, FCT, PRAXIS/PCEX/P/MAT/3996

Randomness in Deterministic Dynamical Systems and Applications PTDC/MAT/105448/2008

Awards

Year Award Awarding entity
1993 bolsa pós-doutoramento programa Human Capital and Mobility
1989 bolsa doutoramento INIC/JNICT

Publications

Livros (autor)

  • Pedro Duarte, Silvius Klein, Lyapunov Exponents of Linear Cocycles: Continuity via Large Deviations. Atlantis Series in Dynamical Systems, ISBN 978-94-6239-124-6.

    Pedro Duarte and Silvius Klein. Continuity of the Lyapunov exponents of lsinear cocycles. Publicações Matemáticas 31º Colóquio Brasileiro de Matemática. Associação Instituto de Matemática Pura e Aplicada-IMPA, 2017

Publicações em actas de encontros científicos


  • Pedro Duarte, Silvius Klein, Large deviation type estimates for iterates of linear cocycles From “Probability in Dynamics”, Stochastics and Dynamics, Volume No.16, Issue No. 03 (2016).

    Pedro Duarte, Maria Joana Torres, Stability of non-deterministic systems. From "Particle systems to partial differential equations. II", pp 193–207, Springer Proc. Math. Stat., 129, (2015).

    P. Duarte, Hamiltonian Systems on Polyhedra in Dynamics, Games and Science II, in Honor of Maurício Peixoto and David Rand, University of Minho, Braga, Portugal, September 8-12, 2008 Series: Springer Proceedings in Mathematics, Vol. 2 (2011).

    P. Duarte, A Solitaire Pebble Game, Proceedings of the Recreational Mathematics Colloquium I, (Ed.), Ludus (2011), ISBN 978-989-95878-8-5.

    Isabel Nunes, João Pedro Neto, Pedro Duarte and Teresa Chambel, Enhancing Modularity and Feedback in Computer Aided Assessment, 15th International Conference on Computing (CIC\'06) (2006), pp. 240-246

    Isabel Nunes, João Pedro Neto, Pedro Duarte and Teresa Chambel, CATS - Computer Assessable Task System, in Electronic Library of Mathematics of the European Mathematical Society, WebALT2006 proceedings, January (2006).

    Ana Santos, Pedro Duarte, Pedro Santos and Miguel Dionísio, On-line assessment in undergraduate Mathematics, An experiment using the system CAL for generating multiple choice questions, Proceedings of 2nd International Conference on the Teaching of Mathematics, (2002).

Artigos em revistas de circulação internacional com arbitragem científica

  • Pedro Duarte and Silvius Klein. Topological obstructions to dominated splitting for ergodic translations on the higher dimensional torus. To appear in Discrete and Continuous Dynamical Systems

    P. Duarte, S. Klein, Continuity positivity and simplicity of the Lyapunov exponents for linear quasi-periodic cocycles. Journal of European Mathematical Society (2017) (to appear: https://www.ems-ph.org/journals/forthcoming.php?jrn=jems)

    P. Duarte, J. P. Gaivão, M. Soufi, Hyperbolic billiards on polytopes with contracting reflection laws. Discrete and Continuous Dynamical Systems, vol. 37, no. 6 (2017), 3079-3109. (doi:10.3934/dcds.2017132)

    G. Del Magno, J. L. Dias, P. Duarte, J. P. Gaivão, Hyperbolic polygonal billiards with finitely many ergodic SRB measures. Ergodic Theory and Dynamical Systems (doi:10.1017/etds.2016.119)

    Hassan Najafi Alishah, Pedro Duarte, Telmo Peixe, Conservative and Dissipative Polymatrix Games. Journal of Dynamics and Games, vol. 2, no. 2 (2015), 157-185.

    Hassan Najafi Alishah, Pedro Duarte, Hamiltonian Evolutionary Games Journal of Dynamics and Games, vol. 2, no. 1 (2015), 33-49.

    Pedro Duarte, Maria Joana Torres, Eigenvectors of isospectral graph transformations. (2014) To appear in Linear Algebra and its Applications.

    P. Duarte, M. J. Torres, r-Regularity Journal of Mathematical Imaging and Vision, http://dx.doi.org/10.1007/s10851-014-0535-y (2014).

    G. Del Magno, J. L. Dias, P. Duarte, J. P. Gaivão, Ergodicity of polygonal slap maps Nonlinearity 27 (2014), no. 8, 1969–1983.

    P. Duarte, S. Klein, Continuity of the Lyapunov exponents for quasiperiodic cocycles Comm. Math. Phys. 332 (2014), no. 3, 1113–1166.

    P. Duarte, S. Klein, Positive Lyapunov exponents for higher dimensional quasiperiodic cocycles Comm. Math. Phys. 332 (2014), no. 1, 189–219.

    G. Del Magno, J. L. Dias, P. Duarte, J. P. Gaivão, D. Pinheiro, SRB measures for polygonal billiards with contracting reflection laws Comm. Math. Phys. 329 (2014), no. 2, 687–723.

    P. Duarte, M.J. Torres, A Discrete Faà di Bruno's Formula Contribution to Discrete Mathematics, Volume 7, Number 2, Pages 72–83, ISSN 1715-0868 (2012)

    P. Duarte, M.J. Torres, Smoothness of Boundaries of Regular Sets with M. J. Torres, J Math Imaging Vis, DOI 10.1007/s10851-012-0397-0 (2012)

    P. Duarte, T. Peixe, Rank of Stably Dissipative Graphs Linear Algebra Appl. 437 (2012), no. 10, 2573–2586.

    G. Del Magno, J. L. Dias, P. Duarte, J. P. Gaivão, D. Pinheiro, Chaos in the square billiard with a modified reflection law Chaos 22, 026106 (2012)

    A. Baraviera, J. L. Dias, P. Duarte On the Herman--Avila--Bochi formula for Lyapunov exponents of SL(2, R)-cocycles Nonlinearity 24 (2011) 2465-2476.

    M. Bessa, P. Duarte, Abundance of elliptic dynamics on conservative 3-flows Dynamical Systems, Volume 23, Issue 4, pp 409-424, (2008).

    P. Duarte, M.J. Torres, Spectral Stability of Markov systems Nonlinearity 21, pp 381-397, (2008).

    P. Duarte, Elliptic Isles in Families of Area Preserving Maps Ergodic Theory & Dynamical Systems, No. 28, pp 1781-1813, (2008).

    P. Duarte, M.J. Torres, Combinatorial stability of non-deterministic systems Ergodic Theory & Dynamical Systems, No. 26, pp 93-128, (2006).

    P. Duarte, Persistent homoclinic tangencies for maps near the identity Ergodic Theory & Dynamical Systems, No. 20, pp 393-438, (2000).

    P. Duarte, Abundance of elliptic isles at conservative bifurcations Dynamics and Stability of Systems, vol 14, No. 4, pp 339-356, (1999).

    P. Duarte, R.L. Fernandes, W. Oliva, Dynamics on the attractor of Lotka-Volterra equations Journal of Differential Equations 149, pp 143-189 (1998).

    P. Duarte, Plenty of elliptic islands for the standard family of area preserving maps Ann. Inst. Henri Poincaré, vol 11, No. 4, pp 359-459, (1994).


Communications

Comunicações orais por convite

School on Dynamical Systems, ICTP, Trieste, September-1991.
Assistant Lecturer in a course about Variational Methods in Lagrangian Systems by R. Mañe

School on Dynamical Systems, ICTP, Trieste, May-1992. Assistant Lecturer in a course about Homoclinic bifurcations by M. Viana

Workshop on Dynamical Systems, IMPA Rio de Janeiro, August-1993 Title: Persistent homoclinic tangencies for the Standard Map family.

Seminar at KTH, Estocolmo, August-1993, Title: Plenty of elliptic islands in the Standad map family.

Meeting on Dynamical Systems, FCUP, Porto, August-1994.
Title: Abundância de ilhas elípticas no desdobramento de tangências homoclínicas.

International Workshop on Dynamical Systems, ICTP, Trieste, May-1995. Title: Persistent homoclinic tangencies at conservative dynamical systems.

First Meeting of Projecto Praxis de Física Matemática , Universidade de Aveiro, February-1996. Title: Persistência de tangências homoclínicas em dinâmica conservativa.

First Meeting of in Dynamical Systems organized by Centro Internacional de Matemática, Observatório Astronómico, Coimbra, September-1996. Title: Sistemas de Lotka-Volterra.

Seminar at KTH, Estocolmo, September-1997. Title: A conservative Lotka Volterra model with positive topological entropy.

Workshop on Stable periodic orbits and homoclinic tangencies in symplectc systems, WIAAS, Berlim-Alemanha, December-1998. Title: Persistent homoclinic tangencies and elliptic islands in conservative systems.

Seminar at IMPA, Rio de Janeiro-Brasil, Maio-1999, Título: Persistênca de tangências homoclínicas em difeomorfismos simplécticos multi-dimensionais.

Seminar at Univ. Federal de Belo Horizonte, Belo Horizonte-Brasil, May-1999, Title: Persistênca de tangências homoclínicas em difeomorfismos simplécticos multi-dimensionais.

Recent Trends in Dynamics I, FCUP, Porto-Portugal, May-2000.

Recent Trends in Dynamics II, FCUP, Porto-Portugal May-2001, Title: Heteroclinic cycles in simple polytopes.

Recent Trends in Dynamics III, FCUP, Porto-Portugal May-2002, Title: Stability of Markov Chains.

e+Calculus, JEM workshop, FCUL, Lisboa-Portugal, January 2007, Title: A Perspective on Automated Assessment.

Dynamics & Applications, in honour of Mauricio Peixoto and David Rand.
September-2008, Title: Hamiltonian systems on polyhedra.

Recreational Mathematics Colloquium I, University of Évora, April 29th­­ to May 2nd 2009.
Title: A Solitaire Pebble Game.

Seminário de Sistemas Dinâmicos, UFRGS, Porto Alegre-Brasil, Setembro 2009.
Title: Produtos Aleatórios de Matrizes,

ENSPM 2010, Sessão temática de Sistemas Dinâmicos.
Leiria Junho 2010.
Title: Lyapunov Morse Functions on Flag Manifolds.

Elementary Geometry from an Advanced Point of View,
Universidade de Aveiro, Setembro 2011,
Title: Morse Landscapes.

Montevideo Dynamical Systems Conference 2012,
August 2012
Title: Dissipative polygonal billiards

4th IST-IME Meeting, September 2012, Lisboa
Title: Dissipative polygonal billiards.

Advanced School Dynamics, Games and Science II,
ISEG Lisbon, August 2013
Title: Replicator and Lotka-Volterra Systems.

Conference Dynamics, Games and Science II,
F.C.Gulbenkian Lisbon, September 2013
Title: Dynamical embeddings in Lotka-Volterra Systems.

EURO Mini-conference on Optimization
in the Natural Sciences, Univ. Aveiro, February 2014.
Title: Hyperbolic Polyhedral Billiards.

5th Iberian Mathematical Meeting,
Univ Aveiro, October 2014
Title: Continuity of Lyapunov Exponents

Seminário de Sistemas Dinâmicos, FCUP, Porto, Janeiro 2015.
Title: Continuity of Lyapunov Exponents

NTNU, Trondheim, March, 2015.
Title: Large deviation estimates for mixing Markov cocycles,

AMS-EMS-SPM international meeting, Porto, June 2015.
Title: Large deviation estimates for Markovian cocycles

Programa Novos Talentos Gulbenkian, ISEG-Lisboa February, 2015.
Title: Problemas Dinâmicos, Oficina Diagonal

NTNU, Trondheim, September, 2015.
Title: Dissipative Polygonal Billiards

Institut Galilée, Universite de Paris 13, Octobre, 2015.
Title: On the continuity of the Lyapunov exponents

Seminario Sistemas Dinâmicos, CMUP, Univ. Porto, April 2016.
Title: Invariant manifolds for flows on polytopes

NTNU, Trondheim, March, 2016.
Title: Large deviation estimates for mixing Markov systems

Seminario Sistemas Dinâmicos, CMUP, Univ.Porto, April 2016.
Title: Invariant manifolds for flows on polytopes

Seminario Sistemas Dinâmicos, Univ. Evora, June 2016.
Title: Invariant manifolds for flows on polytopes

NTNU, Trondheim, August, 2016.
Title: Isospectral Reduction in Infinite Graphs.

Continuity of the Lyapunov exponents of linear cocycles, Curso avançado, 31º Colóquio Brasileiro de Matemática, IMPA, Rio de Janeiro, August, 2017.

Limitations on the regularity of Lyapunov exponents of linear cocycles, Sessão temática de Sistemas Dinâmicos, 31º Colóquio Brasileiro de Matematica, IMPA, Rio de Janeiro, August, 2017.