The Center-Focus Problem and Reversibility
By Marco Antonio Teixeira, Jiazhong Yang. 2001
57 citations recorded by the source corpus.
In this paper we discuss the relation between time-reversibility and the center/focus problem. We show the following: for any analytic planar system X, if j1X, the one-jet of X, is conjugated to (−y, x) then X is analytically time-reversible if and only if it is a center; if j1X is conjugated to (y, 0), then some sufficient and necessary conditions for X to have a center are given. In particular, the reversibility of certain types of polynomial vector fields is studied.
Subfields: Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/04613404ecddbe2308b4a36f59d8c667b65c79a9
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In Geometry and Topology
- Jaume Llibre
- Jaume Giné Mesa
- Héctor Giacomini
- Xiang Zhang
- Maite Grau
- Isaac A. García
- Douglas Duarte Novaes
- Maoan Han
In Statistical and Nonlinear Physics
- Jaume Giné Mesa
- Jaume Llibre
- Héctor Giacomini
- Maite Grau
- Isaac A. García
- Xiang Zhang
- Maoan Han
- Douglas Duarte Novaes
Citations in the corpus
- Local analytic integrability for nilpotent centers (2003, background): “Teixeira and Yang [17] analysed the relationship between reversibility and the center–focus problem for systems (1) and (2), written in a convenient normal form.”
- The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems (2005, background): “The notion of time-reversibility has been generalized in [34] with the notion of rational reversibility, see also [33].”