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Yayın Discrete dynamical systems over double cross-product Lie groupoids(World Scientific, 2021-03) Esen, Oğul; Sütlü, SerkanDiscrete Euler-Lagrange equations are studied over double cross product Lie groupoids. As such, a geometric framework for the local analysis of a discrete dynamical system is established. The arguments are elucidated on the local discrete dynamics of a gauge groupoid. The discrete Elroy's beanie is studied as a physical example.Yayın Matching of cocycle extensions for second tangent groups(American Institute of Physics Inc., 2022-11-07) Uçgun, Filiz Çağatay; Esen, Oğul; Sütlü, SerkanWe present the second-order tangent group of a Lie group as a cocycle extension of the first-order tangent group. We exhibit matching of the second-order tangent groups of two mutually interacting Lie groups. We examine the cocycle extension character of the matched second-order group and arrive at that matched pair of cocycle extensions is a cocycle extension by itself.
