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 |
Appears in Collections |
OER - Khoa học Tự nhiên |
ABSTRACTS VIEWS
26
FULLTEXT VIEWS
18
Files in This Item: