Effectiveness of the Bendixson–Dulac theorem

Autor: Hector Giacomini, Armengol Gasull

Publikováno v: Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona

22 pages, 30 réf.; We illustrate with several new applications the power and elegance of the Bendixson–Dulac theorem to obtain upper bounds of the number of limit cycles for several families of planar vector fields. In some cases we propose to use

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5aa9f74e02589e845dafd50fd1b978e7
https://doi.org/10.1016/j.jde.2021.10.011

Analytic nilpotent centers as limits of nondegenerate centers revisited

Autor: Hector Giacomini, Isaac A. García, Jaume Llibre, Jaume Giné

Publikováno v: Recercat. Dipósit de la Recerca de Catalunya
instname
Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona
Journal of Mathematical Analysis and Applications
Journal of Mathematical Analysis and Applications, Elsevier, 2016, 441, pp.893-899. ⟨10.1016/j.jmaa.2016.04.046⟩
Repositorio Abierto de la UdL
Universitad de Lleida
Recercat: Dipósit de la Recerca de Catalunya
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)

We prove that all the nilpotent centers of planar analytic differential systems are limit of centers with purely imaginary eigenvalues, and consequently the Poincaré--Liapunov method to detect centers with purely imaginary eigenvalues can be used to

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::51be2b1304b2bc2cdeca718e0b1c018c
http://hdl.handle.net/2072/413429

Solving polynomials with ordinary differential equations

Autor: Hector Giacomini, Armengol Gasull

Publikováno v: Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona

In this work we consider a given root of a family of n -degree polynomials as a one-variable function that depends only on the independent term. Then we prove that this function satisfies several ordinary differential equations (ODE). More concretely

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::df5a51963ebd3b07830d709e9d219e38

Localizing Limit Cycles: From Numeric to Analytical Results

Autor: Maite Grau, Hector Giacomini, Armengol Gasull

Publikováno v: Trends in Mathematics ISBN: 9783030011529

This note presents the results of [4]. It deals with the problem of location and existence of limit cycles for real planar polynomial differential systems. We provide a method to construct Poincare–Bendixson regions by using transversal curves, tha

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::0b2c94722d0f81a09e83f199675b5682
https://doi.org/10.1007/978-3-030-01153-6_2

A proof of Perkoʼs conjectures for the Bogdanov–Takens system

Autor: Set Pérez-González, Armengol Gasull, Joan Torregrosa, Hector Giacomini

Publikováno v: Journal of Differential Equations
Journal of Differential Equations, Elsevier, 2013, 255 (9), pp.2655-2671. 〈10.1016/j.jde.2013.07.006〉
Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona
Recercat: Dipósit de la Recerca de Catalunya
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Recercat. Dipósit de la Recerca de Catalunya
instname
Journal of Differential Equations, Elsevier, 2013, 255 (9), pp.2655-2671. ⟨10.1016/j.jde.2013.07.006⟩

International audience; The Bogdanov-Takens system has at most one limit cycle and, in the parameter space, it exists between a Hopf and a saddle-loop bifurcation curves. The aim of this paper is to prove the Perko's conjectures about some analytic p

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::13813bbe13e5865898c37096a8d0051d
https://doi.org/10.1016/j.jde.2013.07.006