A Geometric Approach to Regular Perturbation Theory with an Application to Hydrodynamics

DOI10.2307/2155054zbMath0849.58055OpenAlexW4244218613MaRDI QIDQ4875803

Carmen C. Chicone

Publication date: 10 November 1996

Full work available at URL: https://doi.org/10.2307/2155054

zbMATH Keywords

periodic solutionsEuler equationLyapunov-Schmidt reductionsteady state solutionsideal fluid

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (10)

Chaos in the incompressible Euler equation on manifolds of high dimension ⋮ Beltrami fields and knotted vortex structures in incompressible fluid flows ⋮ How do conservative backbone curves perturb into forced responses? A Melnikov function analysis ⋮ Poincaré bifurcation of a three-dimensional system ⋮ An index for closed orbits in Beltrami fields ⋮ Unnamed Item ⋮ Existence and stability of kayaking orbits for nematic liquid crystals in simple shear flow ⋮ A note on the first integrals of the ABC system ⋮ Generic multiparameter bifurcation from a manifold ⋮ Bifurcations of periodic orbits, subharmonic solutions and invariant Tori of high-dimensional systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• The topology of stationary curl parallel solutions of Euler's equations
• Lyapunov-Schmidt reductions and Melnikov integrals for bifurcation of periodic solutions in coupled oscillators
• Bifurcations of Nonlinear Oscillations and Frequency Entrainment Near Resonance
• Instability criteria for the flow of an inviscid incompressible fluid
• Instability criteria for steady flows of a perfect fluid
• Periodic Solutions of a System of Coupled Oscillators Near Resonance

This page was built for publication: A Geometric Approach to Regular Perturbation Theory with an Application to Hydrodynamics