Publications

Scientific Interests: Dynamical Systems, in particular conservative and symplectic systems, evolutionary game dynamics, random dynamical systems, billiards and linear cocycles.


Published and accepted papers:

  1. A. T. Baraviera, P. Duarte, M. J. Torres, Stationary Measures on Infinite Graphs , To appear in Communications in Contemporary Mathematics (2021).
  2. G. Del Magno, Gianluigi, J.L. Dias, P. Duarte, J.P. Gaivão, Hyperbolic Polygonal Billiards Close to 1-Dimensional Piecewise Expanding Maps. Journal of Statistical Physics 182 (2021), no. 1, 11 (doi: 10.1007/s10955-020-02673-2).
  3. Hassan Najafi Alishah, Pedro Duarte, Telmo Peixe, Asymptotic Poincaré Maps along the edges of Polytopes. Nonlinearity (2020) Volume 33, Issue 1, pp.469-510 (doi: 10.1088/1361-6544/ab49e6).
  4. P. Duarte, S. Klein, Large deviations for products of random two dimensional matrices   Communications in Mathematical Physics (2020) volume 375, pages 2191–2257(2020) (doi:10.1007/s00220-019-03586-2)
  5. P. Duarte, M. J. Torres, Isospectral Reduction in Infinite Graphs.   Journal of Spectral Theory 10 (2020), no. 3, 955–989 (doi: 10.4171/JST/318)
  6. Pedro Duarte, Manuel Santos, and Silvius Klein. A random cocycle with non Holder Lyapunov exponent. Discrete Contin. Dyn. Syst. 39, no. 8, 4841–4861 (2019) (doi: 10.3934/dcds.2019197)
  7. A. T. Baraviera, P. Duarte, Approximating Lyapunov exponents and stationary measures. Journal of Dynamics and Differential Equations, 31, no. 1, 25–48 (2019) (doi: 10.1007/s10884-018-9724-5)
  8. P. Duarte, S. Klein, Continuity positivity and simplicity of the Lyapunov exponents for linear quasi-periodic cocycles.
    Journal of the European Mathematical Society (JEMS), 21, no. 7, 2051-2106 (2019). ( doi: 10.4171/JEMS/880)
  9. P. Duarte, S. Klein, Topological obstructions to dominated splitting for ergodic translations on the higher dimensional torus.
    Discrete and Continuous Dynamical Systems - A, 38-11, (2018)
  10. 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)
  11. 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, vol. 38, no. 6,(2017), 2062-2085 (doi:10.1017/etds.2016.119)
  12. Hassan Najafi Alishah, Pedro Duarte, Telmo Peixe, Conservative and Dissipative Polymatrix Games. Journal of Dynamics and Games, vol. 2, no. 2 (2015), 157-185.
  13. Hassan Najafi Alishah, Pedro Duarte, Hamiltonian Evolutionary Games Journal of Dynamics and Games, vol. 2, no. 1 (2015), 33-49.
  14. Pedro Duarte, Maria Joana Torres, Eigenvectors of isospectral graph transformations. Linear Algebra and its Applications 474 (2015), 110–123.
  15. P. Duarte, M. J. Torres, r-Regularity Journal of Mathematical Imaging and Vision 51 (2015), no. 3, 451–464.
  16. G. Del Magno, J. L. Dias, P. Duarte, J. P. Gaivão, Ergodicity of polygonal slap maps. Nonlinearity 27 (2014), no. 8, 1969–1983.
  17. P. Duarte, S. Klein, Continuity of the Lyapunov exponents for quasiperiodic cocycles. Comm. Math. Phys. 332 (2014), no. 3, 1113–1166.
  18. 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.
  19. P. Duarte, S. Klein, Positive Lyapunov exponents for higher dimensional quasiperiodic cocycles. Comm. Math. Phys. 332 (2014), no. 1, 189–219.
  20. P. Duarte, M.J. Torres, Smoothness of Boundaries of Regular Sets. Journal of Mathematical Imaging and Vision 48, (2014), 106–113.
  21. 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)
  22. 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.
  23. P. Duarte, T. Peixe, Rank of Stably Dissipative Graphs. Linear Algebra Appl. 437 (2012), no. 10, 2573–2586.
  24. 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)
  25. P. Duarte, Elliptic Isles in Families of Area Preserving Maps. Ergodic Theory & Dynamical Systems, No. 28, pp 1781-1813, (2008).
  26. M. Bessa, P. Duarte, Abundance of elliptic dynamics on conservative 3-flows. Dynamical Systems, Volume 23, Issue 4, pp 409-424, (2008).
  27. P. Duarte, M.J. Torres, Spectral Stability of Markov systems. Nonlinearity 21, pp 381-397, (2008).
  28. P. Duarte, M.J. Torres, Combinatorial stability of non-deterministic systems. Ergodic Theory & Dynamical Systems, No. 26, pp 93-128, (2006).
  29. P. Duarte, Persistent homoclinic tangencies for maps near the identity. Ergodic Theory & Dynamical Systems, No. 20, pp 393-438, (2000).
  30. P. Duarte, Abundance of elliptic isles at conservative bifurcations. Dynamics and Stability of Systems, vol 14, No. 4, pp 339-356, (1999).
  31. P. Duarte, R.L. Fernandes, W. Oliva, Dynamics on the attractor of Lotka-Volterra equations. Journal of Differential Equations 149, pp 143-189 (1998).
  32. 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).



Research monographs:

Pedro Duarte, Silvius Klein, Lyapunov Exponents of Linear Cocycles: Continuity via Large Deviations.
Atlantis Series in Dynamical Systems, ISBN 978-94-6239-124-6.
(Draft versions of this book's chapters can be found on Arxiv.)

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





Book chapters and conference proceedings:
  1. 4. G. Del Magno, J. L. Dias, P. Duarte, J. P. Gaivão, The attractor of piecewise expanding maps of the interval , Stochastics and Dynamics (online) (2019) (doi: 10.1142/S0219493720500094)
  2. 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).
  3. G. Del Magno, J. L. Dias, P. Duarte, J. P. Gaivão, D. Pinheiro, Polygonal billiards with strongly contractive reflection laws: a review of some hyperbolic properties,
    Difference Equations, Discrete Dynamical Systems and Applications, Eds. L. Alseda i Soler et al., Springer Proceedings in Mathematics and Statistics 180, (2016), 179-190.
  4. 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).
  5. P. Duarte, Hamiltonian Systems on Polyhedra. Dynamics, games and science. II, pp 257–274, Springer Proc. Math., 2, (2011).



Unpublished papers:

  1. A. T. Baraviera, P. Duarte, Formulas for Lyapunov exponents. (2012).
  2. P. Duarte, A Class of Morse Functions on Flag Manifolds. (2009).
  3. P. Duarte, M.J. Torres, Extension of functions with bounded finite differences. (2008)
  4. P. Duarte, Dynamics along the edges of simple polyhedrons. (2006)