The Center and Focus Problem: Algebraic Solutions and Hypotheses, M. N. Popa and V.V. Pricop, ISBN: 978-1-032-01725-9 (Hardback)
This book focuses on an old problem of the qualitative theory of differential equations, called the Center and Focus Problem. It is intended for mathematicians, researchers, professors and Ph.D. students working in the field of differential equations, as well as other specialists who are interested in the theory of Lie algebras, commutative graded algebras, the theory of generating functions and Hilbert series. The book reflects the results obtained by the authors in the last decades.
A rather essential result is obtained in solving Poincaré's problem. Namely, there are given the upper estimations of the number of Poincaré-Lyapunov quantities, which are algebraically independent and participate in solving the Center and Focus Problem that have not been known so far. These estimations are equal to Krull dimensions of Sibirsky graded algebras of comitants and invariants of systems of differential equations.
1. Lie Algebra Of Operators Of Centro-Affine Group Representation In The
Coefficient Space Of Polynomial Differential Systems
2. Differential
Equations For Centro-Affine Invariants And Comitants Of Differential Systems
And Their Applications
3. Generating Functions And Hilbert Series For
Sibirsky Graded Algebras Of Comitants And Invariants Of Differential Systems
4. Hilbert Series For Sibirsky Algebras And Krull Dimension For Them
5. About
The Center And Focus Problem
6. On The Upper Bound Of The Number Of
Algebraically Independent Focus Quantities That Take Part In Solving The
Center And Focus Problem For The System s(1,m1,,m`)
7. On The Upper Bound Of
The Number Of Algebraically Independent Focus Quantities That Take Part In
Solving The Center And Focus Problem For Lyapunov System. Bibliography
Appendixes
Popa Mihail Nicolae holds a Ph.D. from Gorky University (now Nizhny Novgorod, Russia). He has served as Director and Deputy Director of Vladimir Andrunachievici Institute of Mathematics and Computer Science (IMCS)) in the Laboratory of Differential Equations. He is Professor at the State University of Tiraspol (based in Chisinau). His scientific interests are related to the invariant processes in the qualitative theory of differential equations, Lie algebras and commutative graded algebras, generating functions and Hilbert series, orbit theory, and Lyapunov stability theory.
Pricop Victor Vasile holds a Ph.D. from Vladimir Andrunachievici Institute of Mathematics and Computer Science. He is professor at the State Institute of International Relations of Moldova. Victor Pricop's scientific interests are related to Lie algebras and graded algebras of invariants and comitants, generating functions and Hilbert series, and applications of algebras to polynomial differential systems.
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