A Morse Index-Maslov Index Theorem for Discrete Lagrangian Systems
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Authors
Kavle, Henry
Date
Type
thesis
Language
eng
Keyword
Morse theory , Maslov index , billiards , dynamical systems , discrete mechanics , lagrangian mechanics , hamiltonian mechanics , symplectic geometry
Alternative Title
Abstract
We develop a discrete analog to Morse theory for discrete Lagrangian systems, including a discrete Morse index theorem and a correspondence theorem between the Morse indices of critical trajectories in discrete Lagrangian systems and the Maslov index of symplectic paths arising in associated discrete linear Hamiltonian systems. We use this correspondence to adapt criteria for linear stability of periodic trajectories in Lagrangian dynamics to this discrete setting. Finally, we apply some of these results to dynamical billiards.
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Queen's University's Thesis/Dissertation Non-Exclusive License for Deposit to QSpace and Library and Archives Canada
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Intellectual Property Guidelines at Queen's University
Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.
ProQuest PhD and Master's Theses International Dissemination Agreement
Intellectual Property Guidelines at Queen's University
Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.