The Center and Focus Problem: Algebraic Solutions and Hypotheses

ISBN-13: 9781032044101 / Angielski / Miękka / 2021 / 210 str.

M. N. Popa; V. V. Pricop

Opis

This book focuses on an old problem of the qualitative theory of differential equations, called the Center and Focus Problem. The book reflects the results obtained by the authors in the last decades.

Spis treści

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

O autorze

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, 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, applications of algebras to polynomial differential systems.