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Criteria for the nonexistence of periodic orbits in planar differential systems
Authors: Jaume Giné and Jaume Llibre
Keywords: periodic orbits, Bendixson, Dulac, Li\'enard equation, angular velocity, planar differential systems
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Keywords: periodic orbits, Bendixson, Dulac, Li\'enard equation, angular velocity, planar differential systems
Abstract
In this work we summarize some well-known criteria for the nonexistence of periodic orbits in planar differential systems. Additionally we present two new criteria and illustrate with examples these criteria.Jaume Giné
Departament de Matem`atica, Universitat de Lleida, Avda.
Jaume II, 69; 25001 Lleida, Catalonia, Spain
E-mail:
Jaume Llibre
Departament de Matem`atiques, Universitat Aut`onoma de
Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain
E-mail:
Departament de Matem`atica, Universitat de Lleida, Avda.
Jaume II, 69; 25001 Lleida, Catalonia, Spain
E-mail:
Jaume Llibre
Departament de Matem`atiques, Universitat Aut`onoma de
Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain
E-mail:
DOI
https://doi.org/10.56415/basm.y2023.i1.p3Fulltext
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Contents
- Criteria for the nonexistence of periodic orbits in planar differential systems
- Some families of quadratic systems with at most one limit cycle
- Time-Reversibility and Ivariants of Some 3-dim Systems
- A survey on local integrability and its regularity
- The bifurcation diagram of the configurations of invariant lines of total multiplicity exactly three in quadratic vector fields
- Counting configurations of limit cycles and centers
