Construction of quasi-periodic solutions of delay differential equations via KAM techniques
From MaRDI portal
Publication:1028284
DOI10.1016/j.jde.2009.03.009zbMath1184.34076OpenAlexW1974358346MaRDI QIDQ1028284
Rafael de la Llave, Xue-Mei Li
Publication date: 30 June 2009
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jde.2009.03.009
perturbationdelay differential equationKAM theoryquasi-periodic solutioninvariant decompositionNewton iteration scheme
Almost and pseudo-almost periodic solutions to functional-differential equations (34K14) Linear functional-differential equations (34K06) Theoretical approximation of solutions to functional-differential equations (34K07) Perturbations of functional-differential equations (34K27)
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Cites Work
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- Existence of quasi-periodic solutions for elliptic equations on a cylindrical domain
- A KAM theorem for Hamiltonian partial differential equations in higher dimensional spaces
- A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: rigorous results
- Quasi-periodic solutions of completely resonant nonlinear wave equations
- Quasi-periodic solutions in a nonlinear Schrödinger equation
- Construction of invariant whiskered tori by a parameterization method. I: Maps and flows in finite dimensions
- On elliptic lower dimensional tori in Hamiltonian systems
- Theory of functional differential equations. 2nd ed
- Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations
- Nearly integrable infinite-dimensional Hamiltonian systems
- Construction of quasi-periodic breathers via KAM technique
- Quasi-periodic solutions of a linear functional-differential equation
- Quasiperiodic solutions of differential-difference equations on a torus
- Construction of invariant whiskered tori by a parameterization method. II: Quasi-periodic and almost periodic breathers in coupled map lattices
- A KAM theorem with applications to partial differential equations of higher dimensions
- Invariant tori in quasi-periodic non-autonomous dynamical systems via Herman's method
- Quasiperiodic solutions for dissipative Boussinesq systems
- Neighborhoods of hyperbolic sets
- On optimal estimates for the solutions of linear difference equations on the circle
- The parameterization method for invariant manifolds I: Manifolds associated to non-resonant subspaces
- KAM theory without action-angle variables
- On Quasi-Periodic Perturbations of Elliptic Equilibrium Points
- Quasi-Periodic Solutions for 1D Schrödinger Equations with Higher Order Nonlinearity
- Partial preservation of frequencies in KAM theory