Projective dynamics of homogeneous systems: local invariants, syzygies and the Global Residue Theorem

Projective dynamics of homogeneous systems: local invariants, syzygies and the Global Residue Theorem

We give an explicit formula for the projective dynamics of planar homogeneous polynomial differential systems in terms of natural local invariants and we establish explicit algebraic connections (syzygies) between these invariants (leading to restrictions on possible global dynamics). We discuss mul...

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Veröffentlicht in:Proceedings of the Edinburgh Mathematical Society 2012-10, Vol.55 (3), p.577-589
Hauptverfasser: Balanov, Z., Kononovich, A., Krasnov, Y.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Dynamical systems
Dynamics
Integrals
Invariants
Joints
Mathematical analysis
Polynomials
Residues
Theorems
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Zusammenfassung:We give an explicit formula for the projective dynamics of planar homogeneous polynomial differential systems in terms of natural local invariants and we establish explicit algebraic connections (syzygies) between these invariants (leading to restrictions on possible global dynamics). We discuss multidimensional generalizations together with applications to the existence of first integrals and bounded solutions.
ISSN:0013-0915
1464-3839
DOI:10.1017/S0013091511000435