Diagrammatic methods in classical perturbation theory
DOI10.1007/978-1-0716-2621-4_122zbMATH Open1548.70006MaRDI QIDQ6599388
Publication date: 6 September 2024
Applications of graph theory (05C90) Bifurcations and instability for nonlinear problems in mechanics (70K50) General perturbation schemes for nonlinear problems in mechanics (70K60) Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Perturbation theories for problems in Hamiltonian and Lagrangian mechanics (70H09) Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems (70-02) Averaging of perturbations for nonlinear problems in mechanics (70K65)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Stability for quasi-periodically perturbed Hill's equations
- Conservation of resonant periodic solutions for the one-dimensional nonlinear Schrödinger equation
- Borel summability and Lindstedt series
- Multidimensional continued fractions, dynamical renormalization and KAM theory
- Nearly integrable infinite-dimensional Hamiltonian systems
- Twistless KAM tori
- Quasi-periodic solutions for two-level systems
- Periodic solutions for completely resonant nonlinear wave equations with Dirichlet boundary conditions
- Renormalization group and field theoretic techniques for the analysis of the Lindstedt series
- Hyperbolic low-dimensional invariant tori and summations of divergent series
- Construction of periodic solutions of nonlinear wave equations with Dirichlet boundary conditions by the Lindstedt series method
- Convergent series expansions for quasi-periodic motions
- Degenerate elliptic resonances
- Integrability of hamiltonian systems on cantor sets
- Degenerate lower-dimensional tori under the Bryuno condition
- Summation of divergent series and Borel summability for strongly dissipative differential equations with periodic or quasiperiodic forcing terms
- Breakdown of Lindstedt expansion for chaotic maps
- Fractional Lindstedt series
- Quasiperiodic attractors, Borel summability and the Bryuno condition for strongly dissipative systems
- BIFURCATION CURVES OF SUBHARMONIC SOLUTIONS AND MELNIKOV THEORY UNDER DEGENERACIES
- A renormalization group for Hamiltonians, with applications to KAM tori
- On the solution of linear differential equations in Lie groups
- Newton's method and periodic solutions of nonlinear wave equations
- TWISTLESS KAM TORI, QUASI FLAT HOMOCLINIC INTERSECTIONS, AND OTHER CANCELLATIONS IN THE PERTURBATION SERIES OF CERTAIN COMPLETELY INTEGRABLE HAMILTONIAN SYSTEMS: A REVIEW
- A field theory approach to Lindstedt series for hyperbolic tori in three time scales problems
- The critical function for the semistandard map
- Whiskered tori with prefixed frequencies and Lyapunov spectrum
- METHODS FOR THE ANALYSIS OF THE LINDSTEDT SERIES FOR KAM TORI AND RENORMALIZABILITY IN CLASSICAL MECHANICS: A review with Some Applications
- Renormalization group in statistical mechanics and mechanics: gauge symmetries and vanishing beta functions
- Renormalization group for one-dimensional fermions. A review on mathematical results
This page was built for publication: Diagrammatic methods in classical perturbation theory
