Towards the theory of Hamiltonian systems with an external action
type: Item
instance of: scholarly article
title: Towards the theory of Hamiltonian systems with an external action
zbMATH Open document ID: 0897.70014
author: Yu. A. Kriksin
published in: Doklady Mathematics
publication date: 1998-10-19T00:00:00Z
review text: The author considers the Hamiltonian system with an external action and \(N\) degrees of freedom. First, he ensures the existence and uniqueness of a solution at least on the positive semiaxis of time. Then he establishes the final boundedness of the total mechanical energy on all solutions. The energy boundedness is very important in applications, because it can serve as a measure of stability of physical systems under structural perturbations. Finally, the author describes asymptotic properties of solutions in the past. If one continues any solution in the past, then the value of the Hamiltonian either increases unboundedly or is uniformly bounded.
Mathematics Subject Classification ID: 70H05
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 1050479
zbMATH Keywords: Cauchy problem
zbMATH Keywords: time semiaxis
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: energy boundedness
reviewed by: Vasile Marinca
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1050479