Cubic systems with invariant affine straight lines of total parallel multiplicity seven
In this article, we study the planar cubic differential systems with invariant affine straight lines of total parallel multiplicity seven. We classify these system according to their geometric properties encoded in the configurations of invariant straight lines. We show that there are only 17 d...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2013-12-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2013/274/abstr.html |
| Summary: | In this article, we study the planar cubic differential systems
with invariant affine straight lines of total parallel
multiplicity seven. We classify these system according to their
geometric properties encoded in the configurations of invariant
straight lines. We show that there are only 17 different
topological phase portraits in the Poincar\'e disc associated to
this family of cubic systems up to a reversal of the sense of
their orbits, and we provide representatives of every class modulo
an affine change of variables and rescaling of the time variable. |
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| ISSN: | 1072-6691 |