Remarks on Periods of Planar Hamiltonian Systems

DOI10.1137/0524009zbMath0769.34032OpenAlexW2003020538MaRDI QIDQ4034152

Franz Rothe

Publication date: 16 May 1993

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0524009

zbMATH Keywords

periodic orbitsbifurcationtwo-point boundary value problemcenter pointnondegeneracy assumptionsenergy-period functionVolterra-Lotka systembending pointsHamiltonians with separated variablesthermodynamical averagesthermodynamical problem

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Inverse problems involving ordinary differential equations (34A55)

Related Items (15)

Mixing in anharmonic potential well ⋮ Monotonicity of the period of a nonlinear oscillator ⋮ First derivative of the period function with applications ⋮ The period function of potential systems of polynomials with real zeros ⋮ Monotonicity of the period function of the Liénard equation of second kind ⋮ The period function of Hamiltonian systems with separable variables ⋮ On the period function of \(x^{\prime\prime}+f(x)x^{\prime2}+g(x)=0\) ⋮ The period functions' higher order derivatives ⋮ On the period function of planar systems with unknown normalizers ⋮ The period function of the generalized Lotka-Volterra centers ⋮ The bifurcation set of the period function of the dehomogenized Loud's centers is bounded ⋮ Criteria to bound the number of critical periods ⋮ Dynamics of the attractor in the Lotka-Volterra equations ⋮ Period function for a class of Hamiltonian systems ⋮ On the reversible quadratic centers with monotonic period function

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