Saddle-Type Blow-Up Solutions with Computer-Assisted Proofs Validation and Extraction of Global Nature
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Springer
2023
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| Truy cập trực tuyến: | https://link.springer.com/article/10.1007/s00332-023-09900-6 https://dlib.phenikaa-uni.edu.vn/handle/PNK/7637 |
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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 |
8.891695 |