TY - JOUR
T1 - Projective dynamics of homogeneous systems
T2 - Local invariants, syzygies and the Global Residue Theorem
AU - Balanov, Z.
AU - Kononovich, A.
AU - Krasnov, Y.
PY - 2012/10
Y1 - 2012/10
N2 - 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.
AB - 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.
KW - Euler-Jacobi Theorem
KW - Global Residue Theorem
KW - homogeneous polynomial systems
KW - local invariants
KW - projective dynamics
KW - syzygies
UR - http://www.scopus.com/inward/record.url?scp=84872089242&partnerID=8YFLogxK
U2 - 10.1017/S0013091511000435
DO - 10.1017/S0013091511000435
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AN - SCOPUS:84872089242
SN - 0013-0915
VL - 55
SP - 577
EP - 589
JO - Proceedings of the Edinburgh Mathematical Society
JF - Proceedings of the Edinburgh Mathematical Society
IS - 3
ER -