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Saddle-Type Blow-Up Solutions with Computer-Assisted Proofs Validation and Extraction of Global Nature

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Bibliographic Details
Main Authors: Jean-Philippe, Lessard, Kaname, Matsue, Akitoshi, Takayasu
Format: Book
Language:English
Published: Springer 2023
Subjects:
ODEs
global-in-time solutions
Online Access:https://link.springer.com/article/10.1007/s00332-023-09900-6
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7637
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spelling oai:localhost:PNK-76372023-04-06T04:46:59Z Saddle-Type Blow-Up Solutions with Computer-Assisted Proofs Validation and Extraction of Global Nature Jean-Philippe, Lessard Kaname, Matsue Akitoshi, Takayasu ODEs global-in-time solutions CC BY 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. 2023-04-06T04:46:59Z 2023-04-06T04:46:59Z 2023 Book https://link.springer.com/article/10.1007/s00332-023-09900-6 https://dlib.phenikaa-uni.edu.vn/handle/PNK/7637 en application/pdf Springer
institution Digital Phenikaa
collection Digital Phenikaa
language English
topic ODEs
global-in-time solutions
spellingShingle ODEs
global-in-time solutions
Jean-Philippe, Lessard
Kaname, Matsue
Akitoshi, Takayasu
Saddle-Type Blow-Up Solutions with Computer-Assisted Proofs Validation and Extraction of Global Nature
description CC BY
format Book
author Jean-Philippe, Lessard
Kaname, Matsue
Akitoshi, Takayasu
author_facet Jean-Philippe, Lessard
Kaname, Matsue
Akitoshi, Takayasu
author_sort Jean-Philippe, Lessard
title Saddle-Type Blow-Up Solutions with Computer-Assisted Proofs Validation and Extraction of Global Nature
title_short Saddle-Type Blow-Up Solutions with Computer-Assisted Proofs Validation and Extraction of Global Nature
title_full Saddle-Type Blow-Up Solutions with Computer-Assisted Proofs Validation and Extraction of Global Nature
title_fullStr Saddle-Type Blow-Up Solutions with Computer-Assisted Proofs Validation and Extraction of Global Nature
title_full_unstemmed Saddle-Type Blow-Up Solutions with Computer-Assisted Proofs Validation and Extraction of Global Nature
title_sort saddle-type blow-up solutions with computer-assisted proofs validation and extraction of global nature
publisher Springer
publishDate 2023
url https://link.springer.com/article/10.1007/s00332-023-09900-6
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7637
_version_ 1762456093925048320
score 8.893527

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