The period functionsʼ higher order derivatives
Copyright policy )The period functionsʼ higher order derivatives
We prove a formula for the $n$-th derivative of the period function $T$ in a period annulus of a planar differential system. For $n = 1$, we obtain Freire, Gasull and Guillamon formula for the period's first derivative \cite{FGG}. We apply such a result to hamiltonian systems with separable variables and other systems. We give some sufficient conditions for the period function of conservative second order O.D.E.'s to be convex.
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- University of Trento Italy
Period function, normalizer, period annulus, Linearization, linearization, Period annulus, Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods, Separable variables, Normalizer, Almost and pseudo-almost periodic solutions to ordinary differential equations, separable variables, Period annulus; period function; normalizer; linearization; hamiltonian system; separable variables, Mathematics - Classical Analysis and ODEs, 34C14, 34C15, 37E99, period function, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Hamiltonian system, Periodic solutions to ordinary differential equations, Transformation and reduction of ordinary differential equations and systems, normal forms, Analysis
Period function, normalizer, period annulus, Linearization, linearization, Period annulus, Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods, Separable variables, Normalizer, Almost and pseudo-almost periodic solutions to ordinary differential equations, separable variables, Period annulus; period function; normalizer; linearization; hamiltonian system; separable variables, Mathematics - Classical Analysis and ODEs, 34C14, 34C15, 37E99, period function, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Hamiltonian system, Periodic solutions to ordinary differential equations, Transformation and reduction of ordinary differential equations and systems, normal forms, Analysis
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