Bounding the number of remarkable values via Jouanolou's theorem
| Autor: | Guillaume Chèze |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2015 |
| Předmět: |
Polynomial
FOS: Physical sciences Newton polygon Dynamical Systems (math.DS) [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA] 010103 numerical & computational mathematics 01 natural sciences spectrum Jouanolou's theorem Combinatorics Planar Bounding overwatch Classical Analysis and ODEs (math.CA) FOS: Mathematics [NLIN.NLIN-SI]Nonlinear Sciences [physics]/Exactly Solvable and Integrable Systems [nlin.SI] Mathematics - Dynamical Systems 0101 mathematics Mathematics Nonlinear Sciences - Exactly Solvable and Integrable Systems Applied Mathematics 010102 general mathematics Spectrum (functional analysis) First integrals remarkable values Term (logic) Mathematics - Classical Analysis and ODEs Vector field Exactly Solvable and Integrable Systems (nlin.SI) Analysis |
| Zdroj: | Journal of Differential Equations Journal of Differential Equations, 2015, ⟨10.1016/j.jde.2015.01.027⟩ Journal of Differential Equations, Elsevier, 2015, ⟨10.1016/j.jde.2015.01.027⟩ |
| ISSN: | 0022-0396 1090-2732 |
| DOI: | 10.1016/j.jde.2015.01.027 |
| Popis: | International audience; In this article we bound the number of remarkable values of a polynomial vector field. The proof is short and based on Jouanolou's theorem about rational first integrals of planar polynomial derivations. Our bound is given in term of the size of a Newton polygon associated to the vector field. We prove that this bound is almost reached. |
| Databáze: | OpenAIRE |
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