On a variant of Hilbert’s 16th problem
Abstract We study the number of limit cycles that a planar polynomial vector field can have as a function of its number m of monomials. We prove that the number of limit cycles increases at least quadratically with m and we provide good lower bounds for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>m</mml:mi> <mml:mtext>⩽</mml:mtext> <mml:mn>10</mml:mn> </mml:mrow> </mml:math> .
Authors
- Armengol Gasull (ORCID: https://orcid.org/0000-0002-1719-8231)
- Paulo Santana (ORCID: https://orcid.org/0000-0001-6942-351X)
Institutions
- Universitat Autònoma de Barcelona (ES)
- Centre de Recerca Matemàtica (ES)
- Centro Universitário de Rio Preto (BR)
Publication Details
- Journal
- Nonlinearity
- Published
- 2024-11-06
- DOI
- https://doi.org/10.1088/1361-6544/ad8c1b
- Citations
- 1
- Primary Topic
- Advanced Differential Equations and Dynamical Systems
- Type
- article
- Field-Weighted Citation Impact
- 1.01
Funders
- Fundação de Amparo à Pesquisa do Estado de São Paulo
- Agència de Gestió d'Ajuts Universitaris i de Recerca
- Agencia Estatal de Investigación