Singular dynamics on manifolds: A Cartesian product approach to homotopy group
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Abstract
In this paper, we present the induced singular dynamics of the Cartesian product manifold and their homotopy groups. We also analyze the induced limit singular dynamics on the Cartesian product of manifolds and their associated homotopy group. The role played by the dynamical manifold in the wedge sum of manifolds and their homotopy group will be identified. We introduce a certain type of conditional singular dynamical manifold for free group elements and its homotopy group. Theorems concerning these relations are provided. The results we achieved provide new insights into the relationship between singular dynamics and topology by highlighting how a system's history reflects the algebraic structure of its core manifold.
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