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• W2050184637 abstract "We study vector fields on the plane having only isochronous centres. The most familiar examples are isochronous vector fields, they are the real parts of complex polynomial vector fields on having all their zeroes of centre type. We describe the number of topologically inequivalent isochronous (singular) foliations that can appear for degree s, up to orientation preserving homeomorphisms. For each s, there exists a real analytic variety parametrizing the isochronous vector fields of degree s, the group of complex automorphisms of the plane acts on it. Furthermore, if , then is a non-singular real analytic variety of dimension , and their number of connected components is bounded by . An explicit formula for the residues of the rational 1-form, canonically associated with a complex polynomial vector field with simple zeroes, is given. A collection of residues (i.e. periods) does not characterize an isochronous vector field, even up to complex automorphisms of . An exact bound for the number of isochronous vector fields, up to , having the same collection of residues (periods) is given. We develop several descriptions of the quotient space using residues, weighted s-trees and singular flat Riemannian metrics associated with isochronous vector fields." @default.
• W2050184637 created "2016-06-24" @default.
• W2050184637 creator A5001941364 @default.
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• W2050184637 date "2013-10-01" @default.
• W2050184637 modified "2023-09-27" @default.
• W2050184637 title "Topological and analytical classification of vector fields with only isochronous centres" @default.
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• W2050184637 doi "https://doi.org/10.1080/10236198.2013.772598" @default.
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