INFINITE DIMENSIONAL KRAWCZYK OPERATOR FOR FINDING PERIODIC ORBITS OF DISCRETE DYNAMICAL SYSTEMS

DOI10.1142/S0218127407019937zbMath1148.37041OpenAlexW1978475451MaRDI QIDQ3520715

Zbigniew Galias, Piotr Zgliczyński

Publication date: 26 August 2008

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127407019937

zbMATH Keywords

fixed pointszerosinfinite-dimensional systemsinterval arithmeticKrawczyk methodKot-Schaffer growth-dispersal modellow-period cycles

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Dynamical systems in biology (37N25) Population dynamics (general) (92D25) Interval and finite arithmetic (65G30) Periodic orbits of vector fields and flows (37C27) Approximation methods and numerical treatment of dynamical systems (37M99)

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Microscopic patterns in the 2D phase-field-crystal model ⋮ Fourier-Taylor parameterization of unstable manifolds for parabolic partial differential equations: formalism, implementation and rigorous validation ⋮ Connecting Orbits for Compact Infinite Dimensional Maps: Computer Assisted Proofs of Existence ⋮ A rigorous implicit \(C^1\) Chebyshev integrator for delay equations ⋮ High-Order Parameterization of Stable/Unstable Manifolds for Long Periodic Orbits of Maps ⋮ A functional analytic approach to validated numerics for eigenvalues of delay equations ⋮ Fourier-Taylor approximation of unstable manifolds for compact maps: numerical implementation and computer-assisted error bounds ⋮ Periodic orbits in Hořava-Lifshitz cosmologies ⋮ A proof of Jones' conjecture ⋮ Computational fixed-point theory for differential delay equations with multiple time lags ⋮ Rigorous numerics for NLS: bound states, spectra, and controllability ⋮ Automatic differentiation for Fourier series and the radii polynomial approach

Cites Work

• Discrete-time growth-dispersal models
• Proving the existence of long periodic orbits in 1D maps using interval Newton method and backward shooting
• Interval Methods for Systems of Equations
• A Numerical Verification Method for Solutions of Boundary Value Problems with Local Uniqueness by Banach's Fixed-Point Theorem
• A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems
• Rigorous investigation of the Ikeda map by means of interval arithmetic
• INTERVAL METHODS FOR RIGOROUS INVESTIGATIONS OF PERIODIC ORBITS
• Unnamed Item

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