Iteration inequalities of the Maslov P-index theory with applications. (November 2015)

• Record Type: Journal Article
• Authors: Liu, Chungen; Tang, Shanshan
• Is Part Of: Nonlinear analysis. Volume 127(2015)
• Page Start: 215
• Page End: 234
• Publication Date: 2015-11
• Subjects: 58F05 -- 58E05 -- 34C25 -- 58F10; Maslov P-index -- Iteration inequality -- Minimal period problem -- P-symmetric periodic solution -- Hamiltonian systems; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.06.029
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, the P -splitting numbers and P -mean index for a symplectic path starting from the identity with P ∈ S p ( 2 n ) are defined first, and then by using the Maslov ( P, ω ) -index theory for a symplectic path, various inequalities of the Maslov P -index theory for iterations of symplectic paths starting from the identity are established. As an application, these results are used to study the minimal period problem of P -symmetric periodic solution of nonlinear autonomous Hamiltonian systems.