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On the period function for a family of complex differential equations |
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| Authors: | Antonio Garijo Armengol Gasull |
| Affiliation: | a Dep. d’Eng. Informàtica i Matemàtiques, Universitat Rovira i Virgili, Av. Països Catalans, 26, 43007 Tarragona, Spain b Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain c Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via, 585, 08007 Barcelona, Spain |
| Abstract: | We consider planar differential equations of the form  being f(z) and g(z) holomorphic functions and prove that if g(z) is not constant then for any continuum of period orbits the period function has at most one isolated critical period, which is a minimum. Among other implications, the paper extends a well-known result for meromorphic equations,  that says that any continuum of periodic orbits has a constant period function. |
| Keywords: | primary: 32M25 secondary: 34C25, 37C27 |
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