Abstract
We consider planar differential equations of the form over(z, ̇) = f ( z ) g ( over(z, -) ) 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, over(z, ̇) = h ( z ), that says that any continuum of periodic orbits has a constant period function. © 2005 Elsevier Inc. All rights reserved.
Original language | English |
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Pages (from-to) | 314-331 |
Journal | Journal of Differential Equations |
Volume | 224 |
DOIs | |
Publication status | Published - 15 May 2006 |
Keywords
- Critical period
- Meromorphic vector fields
- Period function
- Periodic orbit