De Poincaré a May: El nacimiento de la Dinámica Discreta

• Autores: Oscar Eduardo Martínez Castiblanco, Primitivo Belén Acosta Humánez
• Localización: MATUA: Revista de matemática de la universidad del Atlántico, ISSN-e 2389-7422, Vol. 7, Nº. 1, 2020 (Ejemplar dedicado a: Revista MATUA), págs. 19-35
• Idioma: español
• Títulos paralelos:
  • From Poincaré to May: The Genesis of Discrete Dynamics
• Enlaces
  • Texto completo
• Resumen
  • español

    En este art ́ıculo, se establece el origen de los sistemas dina ́micos discretos desde una perspectiva histo ́rica, as ́ı como sus ideas seminales: puntos fijos y perio ́dicos, comportamiento cao ́tico, bifurcaciones. Este viaje comienza con los trabajos de Poincare ́ y termina con la obra de May, uno de los art ́ıculos cient ́ıficos mas importantes del siglo XX.

    Este art ́ıculo esta ́ basado en la tesis de Maestr ́ıa ”Simple Permutatios, Pasting and Reversing”([22]), presentada por el primer autor bajo la direccio ́n del segundo autor.

  • English

    In this paper, the origin of discrete dynamics is stated from a historical point of view, as well as its main ideas: fixed and periodic points, chaotic behaviour, bifurcations. This travel will begin with Poincare ́’s work and will finish with May’s work, one of the most important scientific papers of 20th century.

    This paper is based on the M.Sc. thesis ”Simple Permutations, Pasting and Reversing”([22]), written by the first author under the guidance of the second author.

• Referencias bibliográficas
  • Referencias M. F. Acosta-Huma ́nez, P. B. Acosta-Huma ́nez & E. Tuira ́n, Generalized Lennard-Jones Potentials, SUSYQM and Differential...
  • P.Acosta-Huma ́nez,Genealogyofsimplepermutationswithorderapoweroftwo(Spanish).Revista Colombiana de Matema ́ticas, 2 (2008), 1–14.
  • P. Acosta-Huma ́nez, Pasting operation and the square of natural numbers (Spanish). Civilizar, 2 (2003), 85–97.
  • P.B.Acosta-Huma ́nez,Me ́todosalgebraicosensistemasdina ́micos.EdicionesUniversidaddelAtla ́nti- co, EMALCA, (2014).
  • P. B. Acosta-Huma ́nez. Nonautonomous Hamiltonian Systems and Morales-Ramis Theory I. The Case x ̈ = f (x, t). SIAM Journal on Applied...
  • P. B. Acosta-Huma ́nez, M. Alvarez-Ram ́ırez, D. Bla ́zquez-Sanz & J. Delgado. Non-integrability crite- rium for normal variational equations...
  • P. Acosta-Huma ́nez, M. Alvarez-Ram ́ırez & T. J. Stuchi. Nonintegrability of the Armbruster– Guckenheimer–Kim Quartic Hamiltonian Through...
  • P. Acosta-Huma ́nez, A. Chuquen, Pasting and Reversing Approach to Matrix Theory . JP Journal of Algebra, Number Theory and Applications,...
  • ́P.Acosta-Huma ́nez,A.Chuquen,A.Rodr ́ıguez,OnPastingandReversingoperationsoversomerings, Bolet ́ın de Matema ́ticas Universidad Nacional,...
  • P. Acosta-Huma ́nez, O.E. Mart ́ınez Castiblanco, Simple Permutations with Order 4n+2 by Means of Pasting and Reversing Qual. Theory Dyn....
  • K. Alligood, T. Sauer and J. Yorke, Chaos - An introduction to dynamical systems, Textbooks in mathematicas sciences, Springer-Verlag New...
  • P. Blanchard, R.L. Devaney, and G.R. Hall., Differential Equations Belmont, CA: Thomson Brooks/Cole, (2006).
  • R.L. Devaney, An Introduction to Chaotic Dynamical Systems Addison-Wesley Publishing Company, (1989).
  • M.Heno ́n,ATwo-dimensionalMappingwithaStrangeAttractor.CommunicationsinMathematical Physics. Vol 50 Num. 1 , 1976.
  • V. Katz, A history of Mathematics: an introduction Addison-Wesley Educational Publishers, Inc. (1998).
  • T-Y Li, J.A. Yorke, Period Three Implies Chaos. The American Mathematical Monthly, Vol. 82, No. 10. (Dec., 1975), pp. 985-992.
  • E.N. Lorenz, Deterministic Nonperiodic Flow. Journal of the Atmospheric Sciences Vol. 2 Num. 2 , 1963.
  • R.Lozi,UnAttracteurEtrange(?)DuTypeAttracteurdeHe ́non.J.Phys.Colloques.Vol39Num.C5 1978.
  • O.E.Mart ́ınezCastiblanco,Acosta-Huma ́nez,Primitivo,Unenfoquegeome ́tricodelteoremadeShar- kovskii. En Perry, Patricia (Ed.), Memorias del...
  • O.E.Mart ́ınezCastiblanco,SimplePermutations,PastingandReversing.TrabajodeGradopresentado como requisito para optar al t ́ıtulo de Magister...
  • R. May, Simple Mathematical Models With Very Complicated Dynamics. Nature. Vol 261, Num. 459, 1976.
  • M. Misiurewicz, Strange Attractors For The Lozi Mappings. Annals of the New York Academy of Sciences. Vol 357 Num. 1 , 1980.
  • H. Poincare ́, Sur le proble`me des trois corps et les e ́quations de la dynamique, Acta mathematica, Volume 13, (1890), 1–270
  • J-C.Yoccoz,PolynoˆmesquadratiquesetattracteurdeHe ́nonSe ́minaireN.Bourbaki.Exp.734,1990- 1991.