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Welington de Melo (1946–2016)

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New Trends in One-Dimensional Dynamics

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 285))

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Abstract

In memorian: Welington de Melo

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Publications of Welington de Melo

  1. J. Palis Jr., W. de Melo, Introdução aos sistemas dinâmicos, in Projeto Euclides [Euclid Project], vol. 6 (Instituto de Matemática Pura e Aplicada, Rio de Janeiro, 1978)

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  2. J. Palis Jr., W. de Melo, Geometric Theory of Dynamical Systems (Springer, Heidelberg, 1982) [An introduction] (Translated from the Portuguese by A.K. Manning)

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  3. Zh. Palis, V. di Melu, Геометрическаятеориядинамическихсистем. СовременнаяМатематика: ВводныеКурсы. [Contemporary Mathematics: Introductory Courses]. “Mir”, Moscow, 1986. Вvedenie. [An introduction] (Translated from the English by V.N. Kolokoltsov, Translation edited and with notes and an afterword by D.V. Anosov)

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  4. W. de Melo, S. van Strien, One-dimensional dynamics, in Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 25 (Springer, Heidelberg, 1993)

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  5. E. de Faria, W. de Melo, One Dimensional Dynamics: The Mathematical Tools. Publicações Matemáticas do IMPA. [IMPA Mathematical Publications] (Instituto de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, 2001). 23o Colóquio Brasileiro de Matemática [D23rd Brazilian Mathematics Colloquium]

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  6. E. de Faria, W. de Melo, Mathematical Aspects of Quantum Field Theory. Publicações Matemáticas do IMPA. [IMPA Mathematical Publications] (Instituto Nacional de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, 2007) (With a foreword by Dennis Sullivan, 26o Colóquio Brasileiro de Matemática) [26th Brazilian Mathematics Colloquium]

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  7. E. de Faria, W. de Melo, Mathematical tools for one-dimensional dynamics, in Cambridge Studies in Advanced Mathematics, vol. 115 (Cambridge University Press, Cambridge, 2008)

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  8. E. de Faria, W. de Melo, Mathematical aspects of quantum field theory, in Cambridge Studies in Advanced Mathematics, vol. 127 (Cambridge University Press, Cambridge, 2010) (With a foreword by Dennis Sullivan)

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  9. W. de Melo, Structural stability of diffeomorphisms on two-manifolds. Invent. Math. 21, 233–246 (1973)

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  10. W. de Melo, Structural stability on two-manifolds, in Dynamical systems (Proc. Sympos., Univ. Bahia, Salvador, 1971) (Academic Press, New York, 1973) pp. 255–257

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  11. W. de Melo, On the structure of the pareto set of generic mappings. Bol. Soc. Brasil. Mat. 7(2), 121–126 (1976)

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  12. W. de Melo, Stability and optimization of several functions. Topology 15(1), 1–12 (1976)

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  13. W. de Melo, Accessibility of an optimum. Lect. Notes Math. 597, 429–440 (1977)

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  14. C. Gutiérrez, W. de Melo, The connected components of Morse-Smale vector fields on two manifolds. Lect. Notes Math. 597, 230–251 (1977)

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  15. A. Lins, W. de Melo, C.C. Pugh, On Liénard’s equation. Lect. Notes Math. 597, 335–357 (1977)

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  16. W. de Melo, Moduli of stability of two-dimensional diffeomorphisms. Topology 19(1), 9–21 (1980)

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  17. W. de Melo, J. Palis, Moduli of stability for diffeomorphisms. In Global Theory of Dynamical Systems (Proc. Internat. Conf., Northwestern Univ., Evanston, Ill., 1979). Lect. Notes Math. vol. 819 (Springer, Heidelberg, 1980), pp. 318–339

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  18. W. de Melo, J. Palis, S.J. van Strien, Characterising diffeomorphisms with modulus of stability one. In Dynamical Systems and Turbulence, Warwick 1980 (Coventry, 1979/1980), Lect. Notes Math. vol. 898 (Springer, Heidelberg, 1981), pp. 266–285

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  19. W. de Melo, G.L. dos Reis, P. Mendes, Equivariant diffeomorphisms with simple recurrences on two-manifolds. Trans. Amer. Math. Soc. 289(2), 793–807 (1985)

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  20. W. de Melo, A finiteness problem for one-dimensional maps. Proc. Amer. Math. Soc. 101(4), 721–727 (1987)

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  21. W. de Melo, S.J. van Strien, Diffeomorphisms on surfaces with a finite number of moduli. Ergod. Theory Dyn. Syst. 7(3), 415–462 (1987)

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  22. W. de Melo, F. Dumortier, A type of moduli for saddle connections of planar diffeomorphisms. J. Differ. Equ. 75(1), 88–102 (1988)

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  23. W. de Melo, S. van Strien, One-dimensional dynamics: the Schwarzian derivative and beyond. Bull. Amer. Math. Soc. (N.S.) 18(2):159–162 (1988)

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  24. W. de Melo, S. van Strien, A structure theorem in one-dimensional dynamics. Ann. Math. 129(3), 519–546 (1989)

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  25. M. Martens, S. van Strien, W. de Melo, P. Mendes, On cherry flows. Ergod. Theory Dyn. Syst. 10(3), 531–554 (1990)

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  26. M. Martens, W. de Melo, S. van Strien, Julia-Fatou-Sullivan theory for real one-dimensional dynamics. Acta Math. 168(3–4), 273–318 (1992)

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  27. W. de Melo, C. Pugh, The \(C^1\) Brunovský hypothesis. J. Differ. Equ. 113(2), 300–337 (1994)

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  28. W. de Melo, Full families of circle endomorphisms. In Dynamical Systems and Chaos (Hachioji, 1994), vol. 1 (World Sci. Publ., River Edge, NJ, 1995), pp. 25–27

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  29. W. de Melo, B.F. Svaiter, The cost of computing integers. Proc. Amer. Math. Soc. 124(5), 1377–1378 (1996)

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  30. W. de Melo, On the cyclicity of recurrent flows on surfaces. Nonlinearity 10(2), 311–319 (1997)

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  31. W. de Melo, Rigidity and renormalization in one-dimensional dynamical systems. In Proceedings of the International Congress of Mathematicians, vol. II (Berlin, 1998), number extra vol. II, pp. 765–778

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  32. E. de Faria, W. de Melo, Rigidity of critical circle mappings I. J. Eur. Math. Soc. (JEMS) 1(4), 339–392 (1999)

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  33. W. de Melo, A.A. Pinto, Rigidity of \(C^2\) infinitely renormalizable unimodal maps. Comm. Math. Phys. 208(1), 91–105 (1999)

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  34. E. de Faria, W. de Melo, Rigidity of critical circle mappings II. J. Amer. Math. Soc. 13(2), 343–370 (2000)

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  35. A. Avila, W. de Melo, M. Martens, On the dynamics of the renormalization operator. In Global Analysis of Dynamical Systems (Inst. Phys., Bristol, 2001), pp. 449–460

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  36. M. Martens, W. de Melo, Universal models for Lorenz maps. Ergod. Theory Dyn. Syst. 21(3), 833–860 (2001)

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  37. A. Avila, M. Lyubich, W. de Melo, Regular or stochastic dynamics in real analytic families of unimodal maps. Invent. Math. 154(3), 451–550 (2003)

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  38. W. de Melo, Bifurcation of unimodal maps. Qual. Theory Dyn. Syst. 4(2):413–424 (2004)

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  39. E. de Faria, W. de Melo, A. Pinto, Global hyperbolicity of renormalization for \(C^r\) unimodal mappings. Ann. Math. 164(3), 731–824 (2006)

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  40. W. de Melo, Rigidity in dynamics. Bull. Belg. Math. Soc. Simon Stevin 15(5, Dynamics in perturbations), 789–796 (2008)

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  41. V.V.M.S. Chandramouli, M. Martens, W. de Melo, C.P. Tresser, Chaotic period doubling. Ergod. Theory Dyn. Syst. 29(2), 381–418 (2009)

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  42. W. de Melo, Dynamics on the circle. In Dynamics, Games and Science I, Springer Proc. Math. vol. 1 (Springer, Heidelberg, 2011), pp. 651–659

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  43. W. de Melo, Fine structure of hyperbolic diffeomorphisms [book review of mr2464147]. Bull. Amer. Math. Soc. (N.S.) 48(1), 131–136 (2011)

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  44. W. de Melo, Renormalization in one-dimensional dynamics. J. Differ. Equ. Appl. 17(8), 1185–1197 (2011)

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  45. W. de Melo, P.A.S. Salomão, E. Vargas, A full family of multimodal maps on the circle. Ergod. Theory Dyn. Syst. 31(5), 1325–1344 (2011)

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  46. P. Guarino, W. de Melo, Rigidity of smooth critical circle maps. J. Eur. Math. Soc. (JEMS) 19(6), 1729–1783 (2017)

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  47. P. Guarino, M. Martens, W. de Melo, Rigidity of critical circle maps. Duke Math. J. 167(11), 2125–2188 (2018)

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Author information

Authors and Affiliations

  1. University of São Paulo-USP, São Paulo, Brazil

    Edson de Faria

  2. Imperial College London, London, UK

    Sebastian van Strien

Authors
  1. Edson de Faria
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  2. Sebastian van Strien
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Correspondence to Edson de Faria .

Editor information

Editors and Affiliations

  1. Federal University of Rio de Janeiro IM-UFRJ, Institute of Mathematics, Rio de Janeiro, Brazil

    Maria José Pacifico

  2. Institute of Mathematics and Statistics, Fluminense Federal University, Niterói, Rio de Janeiro, Brazil

    Pablo Guarino

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de Faria, E., van Strien, S. (2019). Welington de Melo (1946–2016). In: Pacifico, M., Guarino, P. (eds) New Trends in One-Dimensional Dynamics. Springer Proceedings in Mathematics & Statistics, vol 285. Springer, Cham. https://doi.org/10.1007/978-3-030-16833-9_2

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