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local invariants

Proceedings of the Edinburgh Mathematical Society (1)

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Projective dynamics of homogeneous systems: local invariants, syzygies and the Global Residue Theorem
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Z. Balanov, A. Kononovich, Y. Krasnov
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 55 / Issue 3 / October 2012

Published online by Cambridge University Press:

16 March 2012, pp. 577-589
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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.