Computer-Assisted Proof of Shil'nikov Homoclinics: With Application to the Lorenz-84 Model
DOI10.1137/16M1079956zbMath1371.34061arXiv1605.07799OpenAlexW2964236143MaRDI QIDQ5349315
Maciej J. Capiński, Anna Wasieczko-Zając
Publication date: 24 August 2017
Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1605.07799
Invariant manifold theory for dynamical systems (37D10) Dynamical systems with hyperbolic orbits and sets (37D05) Invariant manifolds for ordinary differential equations (34C45) Algorithms with automatic result verification (65G20) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)
Related Items (6)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The parameterization method for invariant manifolds. From rigorous results to effective computations
- Beyond the Melnikov method: A computer assisted approach
- Polynomial approximation of one parameter families of (un)stable manifolds with rigorous computer assisted error bounds
- Rigorous numerics for piecewise-smooth systems: a functional analytic approach based on Chebyshev series
- Geometric proof for normally hyperbolic invariant manifolds
- A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: rigorous results
- A parametrization method for the computation of invariant tori and their whiskers in quasi-periodic maps: numerical algorithms
- The existence of Shilnikov homoclinic orbits in the Michelson system: A computer assisted proof
- A Lohner-type algorithm for control systems and ordinary differential inclusions
- Covering relations for multidimensional dynamical systems
- Covering relations for multidimensional dynamical systems. II
- Computer assisted proof of transverse saddle-to-saddle connecting orbits for first order vector fields
- Analytical search for homoclinic bifurcations in the Shimizu-Morioka model
- The parameterization method for invariant manifolds. III: Overview and applications
- Rigorous A Posteriori Computation of (Un)Stable Manifolds and Connecting Orbits for Analytic Maps
- Verification methods: Rigorous results using floating-point arithmetic
- Reliable Computation of Robust Response Tori on the Verge of Breakdown
- Rigorous Numerics for Symmetric Connecting Orbits: Even Homoclinics of the Gray–Scott Equation
- Bifurcations and strange attractors in the Lorenz-84 climate model with seasonal forcing
- BIFURCATION AND PREDICTABILITY ANALYSIS OF A LOW-ORDER ATMOSPHERIC CIRCULATION MODEL
- The parameterization method for invariant manifolds I: Manifolds associated to non-resonant subspaces
- The parameterization method for invariant manifolds II: regularity with respect to parameters
- Different scenarios for hyperbolicity breakdown in quasiperiodic area preserving twist maps
- Baroclinic Flow and the Lorenz-84 Model
- Asymptotic stability with rate conditions for dynamical systems
- A Homoclinic Solution for Excitation Waves on a Contractile Substratum
- Parameterization of Invariant Manifolds for Periodic Orbits I: Efficient Numerics via the Floquet Normal Form
- A CONTRIBUTION TO THE PROBLEM OF THE STRUCTURE OF AN EXTENDED NEIGHBORHOOD OF A ROUGH EQUILIBRIUM STATE OF SADDLE-FOCUS TYPE
- Invariant manifolds
- Elements of applied bifurcation theory
This page was built for publication: Computer-Assisted Proof of Shil'nikov Homoclinics: With Application to the Lorenz-84 Model