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Limit cycles for generalized Abel equations
Gasull Embid, Armengol; Guillamon Grabolosa, Antoni
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
This paper deals with the problem of finding upper bounds on the number of periodic solutions of a class of one-dimensional non-autonomous differential equations: those with the right-hand sides being polynomials of degree n and whose coeficients are real smooth 1-periodic functions. The case n = 3 gives the so-called Abel equations which have been thoroughly studied and are quite understood. We consider two natural generalizations of Abel equations. Our results extend previous works of Lins Neto and Panov and try to step forward in the understanding of the case n > 3. They can be applied, as well, to control the number of limit cycles of some planar ordinary differential equations.
Differential equations
Differentiable dynamical systems
Abel equation
limit cycles
planar differential equations
Equacions diferencials ordinàries
Sistemes dinàmics diferenciables
Classificació AMS::34 Ordinary differential equations::34C Qualitative theory
Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
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