Linear Hamiltonian Dynamic Systems on Time Scales: Sturmian Property of the Principal Solution

Martin Bohner; Ondřej Došlý; Roman Hilscher

doi:10.1016/S0362-546X(01)00228-0

Linear Hamiltonian Dynamic Systems on Time Scales: Sturmian Property of the Principal Solution

Martin Bohner
, Ondřej Došlý
, Roman Hilscher

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

Basic results of the oscillation and transformation theories of linear Hamiltonian dynamic systems on time scales are presented. It is shown that these results incorporate, as particular cases, oscillation and transformation theories of linear hamiltonian differential systems and symplectic difference systems. In the last part of the paper a Sturmian-type property of the principal solution of linear Hamiltonian dynamic Systems is established.

Original language	American English
Journal	Nonlinear Analysis: Theory, Methods and Applications
DOIs	https://doi.org/10.1016/S0362-546X(01)00228-0
State	Published - Jan 1 2001

Keywords

Linear Hamiltonian dynamic System
Time scale
principal solution
roundabout theorem

Disciplines

Mathematics
Statistics and Probability

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https://doi.org/10.1016/S0362-546X(01)00228-0

Cite this

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title = "Linear Hamiltonian Dynamic Systems on Time Scales: Sturmian Property of the Principal Solution",

abstract = " Basic results of the oscillation and transformation theories of linear Hamiltonian dynamic systems on time scales are presented. It is shown that these results incorporate, as particular cases, oscillation and transformation theories of linear hamiltonian differential systems and symplectic difference systems. In the last part of the paper a Sturmian-type property of the principal solution of linear Hamiltonian dynamic Systems is established.",

keywords = "Linear Hamiltonian dynamic System, Time scale, principal solution, roundabout theorem",

author = "Martin Bohner and Ond{\v r}ej Do{\v s}l{\'y} and Roman Hilscher",

year = "2001",

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doi = "10.1016/S0362-546X(01)00228-0",

language = "American English",

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AU - Bohner, Martin

AU - Došlý, Ondřej

AU - Hilscher, Roman

PY - 2001/1/1

Y1 - 2001/1/1

N2 - Basic results of the oscillation and transformation theories of linear Hamiltonian dynamic systems on time scales are presented. It is shown that these results incorporate, as particular cases, oscillation and transformation theories of linear hamiltonian differential systems and symplectic difference systems. In the last part of the paper a Sturmian-type property of the principal solution of linear Hamiltonian dynamic Systems is established.

AB - Basic results of the oscillation and transformation theories of linear Hamiltonian dynamic systems on time scales are presented. It is shown that these results incorporate, as particular cases, oscillation and transformation theories of linear hamiltonian differential systems and symplectic difference systems. In the last part of the paper a Sturmian-type property of the principal solution of linear Hamiltonian dynamic Systems is established.

KW - Linear Hamiltonian dynamic System

KW - Time scale

KW - principal solution

KW - roundabout theorem

UR - https://scholarsmine.mst.edu/math_stat_facwork/131

UR - https://doi.org/10.1016/S0362-546X(01)00228-0

U2 - 10.1016/S0362-546X(01)00228-0

DO - 10.1016/S0362-546X(01)00228-0

M3 - Article

JO - Nonlinear Analysis: Theory, Methods and Applications

JF - Nonlinear Analysis: Theory, Methods and Applications

ER -

Linear Hamiltonian Dynamic Systems on Time Scales: Sturmian Property of the Principal Solution

Abstract

Keywords

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