Item Infomation


Title: 
Saddle-Type Blow-Up Solutions with Computer-Assisted Proofs Validation and Extraction of Global Nature
Authors: 
Jean-Philippe, Lessard
Kaname, Matsue
Akitoshi, Takayasu
Issue Date: 
2023
Publisher: 
Springer
Abstract: 
In this paper, blow-up solutions of autonomous ordinary differential equations (ODEs) which are unstable under perturbations of initial points, referred to as saddle-type blow-up solutions, are studied. Combining dynamical systems machinery (e.g., compactifications, timescale desingularizations of vector fields) with tools from computer-assisted proofs (e.g., rigorous integrators, the parameterization method for invariant manifolds), these blow-up solutions are obtained as trajectories on local stable manifolds of hyperbolic saddle equilibria at infinity. With the help of computer-assisted proofs, global trajectories on stable manifolds, inducing blow-up solutions, provide a global picture organized by global-in-time solutions and blow-up solutions simultaneously.
Description: 
CC BY
URI: 
https://link.springer.com/article/10.1007/s00332-023-09900-6
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7637
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