Pedro Miguel Nunes da Rosa Dias Duarte. Artigos publicados em revistas científicas com arbitragem

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Departamento de Matem´atica

Faculdade de Ciˆencias da Univ. de Lisboa Campo Grande, Edif´ıcio C6, Piso 2 P-1749-016 Lisboa

Telefone: (351) 217500321

Email: pmduarte@ciencias.ulisboa.pt Homepage: webpages.fc.ul.pt/ pmduarte/

Forma¸c˜

ao Acad´

emica

1993 Doutoramento em Matem´atica, (IMPA, Rio de Janeiro) Orientador: Jacob Palis Junior

1989 Provas de capacidade cient´ıfica e aptid˜ao pedag´ogica (FCUL) 1985 Licenciatura em Matem´atica (FCUL)

Interesses Cient´ıficos

Sistemas dinˆamicos e Teoria erg´odica: dinˆamica simpl´etica, sistemas dinˆamicos aleat´orios, dinˆamica de bilhares, teoria de jogos evolucion´arios, expoentes de Lyapunov e cociclos lineares.

Artigos publicados em revistas cient´ıficas com arbitragem

Pedro Duarte and Silvius Klein. Continuity positivity and simplicity of the Lyapunov ex-ponents for linear quasi-periodic cocycles. To appear in Journal of European Mathematical Socicety

M. Soufi P. Duarte, J. P. Gaiv˜ao. Hyperbolic billiards on polytopes with contracting reflec-tion laws. To appear in Discrete and Continuous Dynamical Systems

Gianluigi Del Magno, Jo˜ao Lopes Dias, Pedro Duarte, and Jos´e Pedro Gaiv˜ao. Hyperbolic polygonal billiards with finitely many ergodic srb measures. To appear in Ergodic Theory and Dynamical Systems

Hassan Najafi Alishah, Pedro Duarte, and Telmo Peixe. Conservative and dissipative poly-matrix games. J. Dyn. Games, 2(1):157–185, 2015

Hassan Najafi Alishah and Pedro Duarte. Hamiltonian evolutionary games. J. Dyn. Games, 2(1):33–49, 2015

Pedro Duarte and Maria Joana Torres. Eigenvectors of isospectral graph transformations. Linear Algebra Appl., 474:110–123, 2015

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Pedro Duarte and Silvius Klein. Continuity of the Lyapunov exponents for quasiperiodic cocycles. Comm. Math. Phys., 332(3):1113–1166, 2014

Pedro Duarte and Silvius Klein. Positive Lyapunov exponents for higher dimensional quasiperiodic cocycles. Comm. Math. Phys., 332(1):189–219, 2014

Gianluigi Del Magno, Jo˜ao Lopes Dias, Pedro Duarte, Jos´e Pedro Gaiv˜ao, and Diogo Pin-heiro. SRB measures for polygonal billiards with contracting reflection laws. Comm. Math. Phys., 329(2):687–723, 2014

Pedro Duarte and Maria Joana Torres. r-regularity. J. Math. Imaging Vision, 51(3):451– 464, 2015

Pedro Duarte and Maria Joana Torres. Smoothness of boundaries of regular sets. J. Math. Imaging Vision, 48(1):106–113, 2014

Gianluigi Del Magno, Jo˜ao Lopes Dias, Pedro Duarte, and Jos´e Pedro Gaiv˜ao. Ergodicity of polygonal slap maps. Nonlinearity, 27(8):1969–1983, 2014

Gianluigi Del Magno, Jo˜ao Lopes Dias, Pedro Duarte, Jos´e Pedro Gaiv˜ao, and Diogo Pin-heiro. Chaos in the square billiard with a modified reflection law. Chaos, 22(2), 2012 Pedro Duarte and Telmo Peixe. Rank of stably dissipative graphs. Linear Algebra Appl., 437(10):2573–2586, 2012

Alexandre T. Baraviera, Jo˜ao Lopes Dias, and Pedro Duarte. On the Herman-Avila-Bochi formula for Lyapunov exponents of SL(2, R)-cocycles. Nonlinearity, 24(9):2465–2476, 2011 Pedro Duarte and Maria Joana Torres. A discrete Fa`a di Bruno’s formula. Contrib. Discrete Math., 7(2):72–83, 2012

P. Duarte. Elliptic isles in families of area-preserving maps. Ergodic Theory Dynam. Sys-tems, 28(6):1781–1813, 2008

M´ario Bessa and Pedro Duarte. Abundance of elliptic dynamics on conservative three-flows. Dyn. Syst., 23(4):409–424, 2008

P. Duarte and M. J. Torres. Spectral stability of Markov systems. Nonlinearity, 21(3):381– 397, 2008

P. Duarte and M. J. Torres. Combinatorial stability of non-deterministic systems. Ergodic Theory Dynam. Systems, 26(1):93–128, 2006

Pedro Duarte. Persistent homoclinic tangencies for conservative maps near the identity. Ergodic Theory Dynam. Systems, 20(2):393–438, 2000

Pedro Duarte. Abundance of elliptic isles at conservative bifurcations. Dynam. Stability Systems, 14(4):339–356, 1999

Pedro Duarte, Rui L. Fernandes, and Waldyr M. Oliva. Dynamics of the attractor in the Lotka-Volterra equations. J. Differential Equations, 149(1):143–189, 1998

Pedro Duarte. Plenty of elliptic islands for the standard family of area preserving maps. Ann. Inst. H. Poincar´e Anal. Non Lin´eaire, 11(4):359–409, 1994

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Monografias cient´ıficas

Pedro Duarte and Silvius Klein. Lyapunov exponents of Linear cocycles. Continuity via large deviations. Atlantis Studies in Dynamical Systems. Atlantis Press, Paris, 2016 Pedro Duarte. Existˆencia de Muitas Ilhas El´ıticas para a Fam´ılia Canˆonica de Trans-forma¸c˜oes que Preservam ´Area. PhD thesis, IMPA, Estrada Dona Castorina 110, Rio de Janeiro, Brasil, 1993

Cap´ıtulos de livros (conference proceedings)

Pedro Duarte and Silvius Klein. Large deviation type estimates for iterates of linear cocycles. Stochastics and Dynamics, 16(3), 2016

Pedro Duarte and Maria Joana Torres. Stability of non-deterministic systems. In Patr´ıcia Gon¸calves and Ana Jacinta Soares, editors, From Particle Systems to Partial Differential Equations II, volume 129 of Springer Proceedings in Mathematics & Statistics, pages 193– 207. Springer International Publishing, 2015

Pedro Duarte. Hamiltonian systems on polyhedra. In Dynamics, games and science. II, volume 2 of Springer Proc. Math., pages 257–274. Springer, Heidelberg, 2011

Gianluigi Del Magno, Jo˜ao Lopes Dias, Pedro Duarte, Jos´e Pedro Gaiv˜ao, and Diogo Pin-heiro. Polygonal Billiards with Strongly Contractive Reflection Laws: A Review of Some Hyperbolic Properties, pages 179–190. Springer Berlin Heidelberg, Berlin, Heidelberg, 2016

Outras Publica¸c˜

oes

Pedro Duarte and Alessandro Margheri. Sobrevoando cumes e vales. Gazeta de Matem´atica, (169), 2013

Pedro Duarte and Telmo Peixe. Observar golfinhos...com trignometria. Gazeta de Matem´atica, (169), 2013

Pedro Duarte. Dynamics along the edges of simple polyhedrons. Unpublished manuscript, 2006

Isabel Nunes, Jo˜ao Pedro Neto, Teresa Chambel, and Pedro Duarte. Enhancing modularity and feedback in computer aided assessment. In 15th International Conference on Computing (CIC’ 06), pages 240–246. IEEE, 2006

P. Duarte. Solution to a solitaire game. In Recreational Mathematics Colloquium I, pages 161–171. Assoc. Ludus, Lisbon, 2010

Isabel Nunes, Jo˜ao Pedro Neto, Teresa Chambel, and Pedro Duarte. Cats - computer assessable task system. In M. Sepp¨al¨a, S. Xamb’o, and O. Caprotti, editors, Proceedings of WebALT 2006, First WebALT Conference and Exhibition. Oy WebALT Inc, 2006

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Organiza¸c˜

ao de conferˆ

encias e semin´

arios

Smooth ergodic theory Workshop, IST Lisboa-Portugal, March 1999 Semin´ario de Sistemas Dinˆamicos do CMAF (desde 2007)

1st One Day Meeting on Dynamical Systems, February 9, 2010 2nd One Day Meeting on Dynamical Systems, June 16, 2011 3rd One Day Meeting on Dynamical Systems, December 12, 2012 4th One Day Meeting on Dynamical Systems, May 2, 2013 5th One Day Meeting on Dynamical Systems, February 10, 2014 6th One Day Meeting on Dynamical Systems, January 19, 2015 7th One Day Meeting on Dynamical Systems, March 4, 2016

Conferˆ

encias e semin´

arios por convite

School on Dynamical Systems, ICTP, Trieste, September 1991. Assistant Lecturer in a course about Variational Methods in Lagrangian Systems by R. Ma˜n´e.

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

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

Plenty of elliptic islands in the Standad map family, Seminar at KTH, Estocolmo, August 1993. Abundˆancia de ilhas el´ıpticas no desdobramento de tangˆencias homocl´ınicas, Meeting on Dy-namical Systems, FCUP, Porto, August 1994.

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

Persistˆencia de tangˆencias homocl´ınicas em dinˆamica conservativa, First Meeting of Projecto Praxis de F´ısica Matem´atica , Universidade de Aveiro, February 1996.

Sistemas de Lotka-Volterra, First Meeting of in Dynamical Systems organized by Centro Inter-nacional de Matem´atica, Observat´orio Astron´omico, Coimbra, September 1996.

A conservative Lotka Volterra model with positive topological entropy, Seminar at KTH, Esto-colmo, September 1997.

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

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Persistˆenca de tangˆencias homocl´ınicas em difeomorfismos simpl´ecticos multi-dimensionais, Seminar at IMPA, Rio de Janeiro-Brasil, May 1999.

Um gerador de perguntas de escolha m´ultipla, Jornadas Pedag´ogicas do IST, June 1999. Persistˆenca de tangˆencias homocl´ınicas em difeomorfismos simpl´ecticos multi-dimensionais, Seminar at Univ. Federal de Belo Horizonte, Belo Horizonte-Brasil, May 1999.

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

Stability of Markov Chains, Recent Trends in Dynamics III, FCUP, Porto-Portugal May 2002. A Perspective on Automated Assessmen, e+Calculus, JEM workshop, FCUL, Lisboa-Portugal, January 2007.

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

A Solitaire Pebble Game, Recreational Mathematics Colloquium I, University of ´Evora, April 29th to May 2009.

Produtos Aleat´orios de Matrizes, Semin´ario de Sistemas DInˆamicos, UFRGS, Porto Alegre-Brasil, September 2009.

Lyapunov Morse Functions on Flag Manifolds, Sess˜ao tem´atica de Sistemas Dinˆamicos. ENSPM 2010, Leiria June 2010.

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

Dissipative polygonal billiards, Montevideo Dynamical Systems Conference 2012, August 2012. Dissipative Polygonal Billiards, 4th IST-IME Meeting, Lisboa, September 2012.

Theory of Evolutionary games, Short course: Topics in dynamical systems, DMFCUL April 2013.

Replicator and Lotka-Volterra Systems, School DGS 2013 - Advanced School Planet Earth, Dynamics, Games and Science, Lisboa, August 2013.

Dynamical embeddings in Lotka-Volterra Systems, DGS 2013 - International Conference Planet Earth, Dynamics, Games and Science, Lisboa, September 2013.

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

Continuity of Lyapunov Exponents, 5th Iberian Mathematical Meeting, Aveiro Octobre, 2014. Continuity of Lyapunov Exponents, Semin´ario Sistemas Dinˆamicos, CMUP, Univ. Porto, Jan-uary 2015.

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Large deviation estimates for mixing Markov cocycles, NTNU, Trondheim, March, 2015. Large deviation estimates for Markovian cocycles, AMS-EMS-SPM international meeting, Porto, June 2015.

Problemas Dinˆamicos, Oficina Diagonal, Programa Novos Talentos Gulbenkian, ISEG-Lisboa February, 2015.

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

On the continuity of the Lyapunov exponents, Institut Galil´ee, Universit´e de Paris 13, Octobre, 2015.

Invariant manifolds for flows on polytopes, Semin´ario Sistemas Dinˆamicos, CMUP, Univ. Porto, April 2016.

Large deviation estimates for mixing Markov systems, NTNU, Trondheim, March, 2016. Invariant manifolds for flows on polytopes, Semin´ario Sistemas Dinˆamicos, CMUP, Univ. Porto, April 2016.

Invariant manifolds for flows on polytopes, Semin´ario Sistemas Dinˆamicos, Univ. ´Evora, June 2016.

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

Participa¸c˜

ao em Projectos

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

Variedades diferenci´aveis combinat´oricas, FCT, PRAXIS/PCEX/P/MAT/3996 Randomness in Deterministic Dynamical Systems and Applications,

PTDC/MAT/105448/2008

Bolsas de Estudo

Bolseiro doutoramento INIC/JNICT 1989-1993

Bolseiro p´os-doutoramento, com bolsa do projecto Human Capital and Mobility, Agosto-Dezembro de 1993

Orienta¸c˜

oes de P´

os-Doutoramento

Nuno Matos Luzia (2008-2009) Silvius Klein (Janeiro-Julho de 2013)

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Mohammad Soufi (Janeiro-Julho de 2013) Hassan Alishah (Janeiro-Julho de 2013)

Orienta¸c˜

oes de Doutoramento

Maria Joana Torres, FCUL Julho de 2004, Markov Chains close to maps on compact manifolds Telmo Lucas Peixe, FCUL Novembro de 2015, Lotka-Volterra Systems and Polymatrix Repli-cators

Orienta¸c˜

oes de Mestrado

Paulo Jorge Ferreira de Oliveira Coelho, FCUL Dezembro 2008, Templates e Elos de ´Orbitas Peri´odicas em Fluxos de Dimens˜ao 3.

Telmo Jorge Lucas Peixe, FCUL Dezembro 2010, Sistemas Lotka-Volterra Dissipativos. Jo˜ao Carlos Carmona e Silva, FCUL Outubro 2012, Medida de Erd¨os: Uma Introdu¸c˜ao. Pedro Miguel dos Santos Pinto, (co-orienta¸c˜ao) FCUL Dezembro 2013, Teorema da Estrutura de Furstenberg: demonstra¸c˜ao e redu¸c˜ao ao n´ıvel ωωω.

Outras Orienta¸c˜

oes

Maria Jo˜ao Costa Almeida Quint˜ao Pereira, IST-UTL Outubro 2001, Trabalho de fim de curso: Dinˆamica Adaptativa: Jogos, Estrat´egias Estoc´asticas e Interpreta¸c˜oes Biol´ogicas.

Pedro Pantoja, 2010-2011, Tutoria Programa Novos Talentos. Manuel Santos, 2015-2016, Tutoria Programa Novos Talentos.

Notas de curso

C´alculo (2003-2005)

http://webpages.fc.ul.pt/~pmduarte/Calculo/Informatica/notas_cal.pdf Topologia Diferencial (2006-2011)

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Participa¸c˜

ao em juris de Doutoramento

Ana Maria Alves de S´a, Sobre o conjunto minimal de per´ıodos das aplica¸c˜oes cont´ınuas num bouquet de circunferˆencias, FCT-UNL, Outubro 1994

Francesc Vilamaj´o, Global Dynamics for Families of C2 Endomorphisms in Dimension Greater than One, Universitat Aut`onoma de Barcelona, Setembro 1998

Jo˜ao Lu´ıs Gon¸calves Dias Ferreira Alves, Uma abordagem functorial `a Teoria do Kneading, IST-UTL, Mar¸co 2000

Carla Lopes Dias, Geometry of Hyperbolic Measures and the Liftability Problem, FCUP, Dezembro 2009

M´ario Frengue Getimane, On Random Matrix and its Applications, Escola de Ciˆencias, Univ. do Minho, Janeiro de 2011

Maria de La Salete Dias Esteves, Skew-product maps and Heterodimensional cycles, FCUP, Julho de 2011

Gast˜ao Henrique Gon¸calves de Bettencourt, Random Walks, Boundary Theory and Hilbert’s Metric, Univ. Beira Interior, Julho 2011

Paulo Ricardo Ferreira Pinto, Density of first Poincar´e returns and periodic orbits, FCUP, 2012

Cristina Serpa, Systems of Iterative Functional Equations: Theory and Applications, FCUL 2015.

Participa¸c˜

ao em juris de equivalˆ

encia de Doutoramento

Zaqueu Nogueira Coelho-Filho, Entropy and ergodicity of skew-products and subshifts of finite type and central limit asymptotics. FCUP, Julho, 1997.

Forma¸c˜

ao Cont´ınua

Ac¸c˜oes sobre a utiliza¸c˜ao do Geogebra como ferramenta para o ensino da Matem´atica no 3o ciclo e secund´ario.

(2009-2010) Ac¸c˜ao de Forma¸c˜ao do DM: Da Modela¸c˜ao Matem´atica `a Simula¸c˜ao Computa-cional (ac¸c˜ao de 40 horas)

(2010-2011) Ac¸c˜ao de Forma¸c˜ao DM-Lisboa Editora: A¸c˜ao de Forma¸c˜ao Matem´atica e Tecnologia (ac¸c˜ao de 12.5 horas)

(2012) Ac¸c˜ao de Forma¸c˜ao do DM-Ra´ız Editora: A¸c˜ao de Forma¸c˜ao Matem´atica e Tecnolo-gia - 3.o ciclo e secund´ario (duas ac¸c˜oes de 6 horas cada)

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Competˆ

encias Tecnol´

ogicas

Bom dom´ınio de programa¸c˜ao em Basic, Mathematica, Geogebra, Javascript, Java, Html e Latex. Alguma experiˆencia de programa¸c˜ao em outras linguagens como Excel, Pov-Ray, JavaCC, Maxima, Haskell e Prolog.

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