A multivalued logarithm on time scales
作者：
Highlights：
• In this paper, we address a long-standing open problem on time scales calculus by presenting a new definition of a multivalued logarithm function for dynamic equations on time scales. This new logarithm satisfies many familiar properties when the time scale is R, the real line, properties that previous time-scale logarithms did not satisfy. We also make a connection to Cayley dynamic equations on time scales. Finally, we include an entire section of examples on nontrivial time scales illustrating this new logarithm, and demonstrate its accuracy in a numerical comparison with previous definitions.
摘要
•In this paper, we address a long-standing open problem on time scales calculus by presenting a new definition of a multivalued logarithm function for dynamic equations on time scales. This new logarithm satisfies many familiar properties when the time scale is R, the real line, properties that previous time-scale logarithms did not satisfy. We also make a connection to Cayley dynamic equations on time scales. Finally, we include an entire section of examples on nontrivial time scales illustrating this new logarithm, and demonstrate its accuracy in a numerical comparison with previous definitions.
论文关键词：Dynamic equations,Cylinder transformation,Logarithm,Time scales,Cayley transformation
论文评审过程：Received 16 February 2020, Revised 21 December 2020, Accepted 28 December 2020, Available online 12 January 2021, Version of Record 12 January 2021.
论文官网地址：https://doi.org/10.1016/j.amc.2021.125954
