On some aspects of the Bohl transformation for Hamiltonian and symplectic systems

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• 作者：Ondřej Do&scaron ; lý ; ^{dosly@math.muni.cz}
• 关键词：Bohl transformation ; Trigonometric transformation ; Trigonometric system ; Hyperbolic transformation ; Geometrical oscillation theory
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 April 2017
• 年：2017
• 卷：448
• 期：1
• 页码：281-292
• 全文大小：315 K
• 卷排序：448

文摘

The classical Bohl transformation [4] from 1906 concerns the second order linear differential equations and states, roughly speaking, that a pair of linearly independent solutions of a second order differential equation can be expressed via the sine and cosine functions. Since that time, this transformation has been extended in various directions and became e.g. the theoretical basis for the deeply developed transformation theory of second order linear differential equations [8]. In our paper we discuss this transformation for linear Hamiltonian differential systems and discrete symplectic systems. We provide an alternative proofs to some know results and these new proofs enable to give a new insight into the topics. We also formulate some open problems associated with the discrete Bohl transformation.