Weight Homogeneous A.c.i. Systems
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In this chapter we introduce a class of a.c.i. systems for which everything can be explicitly computed. For these systems, which we will call weight ho-mogeneous a.c.i. systems, phase space is always C n , and a system of linear coordinates on C n can be chosen in such a way that everything (the poly-nomials in involution, the Poisson structure, the commuting vector fields) becomes homogeneous upon assigning weights to each of these coordinates. For these systems we will provide methods by means of which one can reveal the whole geometry of the system and prove (or disprove) algebraic complete integrability.
KeywordsVector Field Irreducible Component Abelian Variety Poisson Structure Laurent Series
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