Name: Counting configurations of limit cycles and centers
Keywords: Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics, Classificació AMS::34 Ordinary differential equations::34C Qualitative theory, Fibonacci numbers, Limit cycle, Sistemes dinàmics diferenciables, Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory, Phase portrait, Fibonacci numbers., Limit cycles, Center

descriptionPublicationkeyboard_double_arrow_right Report 01 Jan 2023 English

Authors: Gasull, Armengol; Guillamon Grabolosa, Antoni; Mañosa Fernández, Víctor;

handle: 2117/390917

Counting configurations of limit cycles and centers

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Abstract

We present several results on the determination of the number and distribution of limit cycles or centers for planar systems of differential equations. In most cases, the study of a recurrence is one of the key points of our approach. These results include the counting of the number of configurations of stabilities of nested limit cycles, the study of the number of different configurations of a given number of limit cycles, the proof of some quadratic lower bounds for Hilbert numbers and some questions about the number of centers for planar polynomial vector fields.

This work has been realized thanks to the Ministerio de Ciencia e Innovación (PID2019-104658GB-I00 and PID2021-122954-I00 grants), the grant Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M) and also the Agència de Gestió d’Ajuts Universitaris i de Recerca (2021 SGR 00113 and 2021 SGR 01039 grants).

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Keywords

Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics, Classificació AMS::34 Ordinary differential equations::34C Qualitative theory, Fibonacci numbers, Limit cycle, Sistemes dinàmics diferenciables, Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory, Phase portrait, Fibonacci numbers., Limit cycles, Center, Recurrence, Differentiable dynamical systems, Configuration, Cicles límits

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