✦ LIBER ✦

Planar analytic vector fields with generalized rational first integrals

✍ Scribed by Weigu Li; Jaume Llibre; Xiang Zhang

Publisher: Elsevier Science
Year: 2001
Tongue: French
Weight: 123 KB
Volume: 125
Category: Article
ISSN: 0007-4497
DOI: 10.1016/s0007-4497(01)01083-1

No coin nor oath required. For personal study only.

✦ Synopsis

The main purpose of this paper is to characterize a germ of planar holomorphic vector field at an elementary singular point having a generalized rational first integral. Our results generalize a result due to Poincaré on a necessary condition of the existence of a rational first integral for planar polynomial systems. As two applications of our main result, we give the necessary and sufficient conditions on the existence of rational first integral for planar quadratic systems having either a weak nondegenerate singular point, or a degenerate elementary singular point.  2001 Éditions scientifiques et médicales Elsevier SAS

📜 SIMILAR VOLUMES

Invariant Algebraic Curves and Rational

Invariant Algebraic Curves and Rational First Integrals for Planar Polynomial Vector Fields

✍ Javier Chavarriga; Jaume Llibre 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 131 KB

## dedicated to professor jack k. hale on the occasion of his 70th birthday We present three main results. The first two provide sufficient conditions in order that a planar polynomial vector field in C 2 has a rational first integral, and the third one studies the number of multiple points that a

Periodic Orbits for Vector Fields with N

Periodic Orbits for Vector Fields with Nondegenerate First Integrals

✍ Massimo Villarini 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 159 KB

Finitely Generated Algebras Associated w

Finitely Generated Algebras Associated with Rational Vector Fields

✍ Hisayo Aoki; Masayoshi Miyanishi 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 257 KB

Phase portraits of quadratic polynomial

Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 3

✍ Jaume Llibre; Regilene D.S. Oliveira 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 977 KB

Phase portraits of quadratic polynomial

Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 2

✍ Laurent Cairó; Jaume Llibre 📂 Article 📅 2007 🏛 Elsevier Science 🌐 English ⚖ 840 KB

We classify all the global phase portraits of the quadratic polynomial vector fields having a rational first integral of degree 2. In other words we characterize all the global phase portraits of the quadratic polynomial vector fields having all their orbits contained in conics. For such a vector fi

Planar polynomial vector fields having a

Planar polynomial vector fields having a polynomial first integral can be obtained from linear systems

✍ Belen García; Héctor Giacomini; Jesús S. Pérez del Río 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 222 KB

We consider in this work planar polynomial differential systems having a polynomial first integral. We prove that these systems can be obtained from a linear system through a polynomial transformation of variables.