Inverse Problems In Ordinary Differential Equations And Applications (progress In Mathematics)
by Jaume Llibre /
2016 / English / PDF
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This book is dedicated to study the inverse problem of ordinary
differential equations, that is it focuses in finding all
ordinary differential equations that satisfy a given set of
properties. The Nambu bracket is the central tool in developing
this approach. The authors start characterizing the ordinary
differential equations in R^N which have a given set of partial
integrals or first integrals. The results obtained are applied
first to planar polynomial differential systems with a given set
of such integrals, second to solve the 16th Hilbert problem
restricted to generic algebraic limit cycles, third for solving
the inverse problem for constrained Lagrangian and Hamiltonian
mechanical systems, fourth for studying the integrability of a
constrained rigid body. Finally the authors conclude with an
analysis on nonholonomic mechanics, a generalization of the
Hamiltonian principle, and the statement an solution of the
inverse problem in vakonomic mechanics.
This book is dedicated to study the inverse problem of ordinary
differential equations, that is it focuses in finding all
ordinary differential equations that satisfy a given set of
properties. The Nambu bracket is the central tool in developing
this approach. The authors start characterizing the ordinary
differential equations in R^N which have a given set of partial
integrals or first integrals. The results obtained are applied
first to planar polynomial differential systems with a given set
of such integrals, second to solve the 16th Hilbert problem
restricted to generic algebraic limit cycles, third for solving
the inverse problem for constrained Lagrangian and Hamiltonian
mechanical systems, fourth for studying the integrability of a
constrained rigid body. Finally the authors conclude with an
analysis on nonholonomic mechanics, a generalization of the
Hamiltonian principle, and the statement an solution of the
inverse problem in vakonomic mechanics.