Phase portraits of quadratic polynomial differential systems having as solution some classical planar algebraic curves of degree 4
Date
2019-01-28
Authors
Benterki, Rebiha
Llibre, Jaume
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We classify the phase portraits of quadratic polynomial differential systems having some relevant classic quartic algebraic curves as invariant algebraic curves, i.e. these curves are formed by orbits of the quadratic polynomial differential system.
More precisely, we realize 16 different well-known algebraic curves of degree 4 as invariant curves inside the quadratic polynomial differential systems. These realizations produce 31 topologically different phase portraits in the Poincare disc for such quadratic polynomial differential systems.
Description
Keywords
Quadratic differential system, Poincare disc, Invariant algebraic curve
Citation
Benterki, R., & Llibre, J. (2019). Phase portraits of quadratic polynomial differential systems having as solution some classical planar algebraic curves of degree 4. <i>Electronic Journal of Differential Equations, 2019</i>(15), pp. 1-25.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.