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Synthetic approach to dynamics
A brief introduction
Future directions.
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Prerequisites.
1) Foundational mathematics : familiatity with proofs and mathematical rigor; set-theory
2) Category theory : functors, categories, natural transformations
3) Analysis : continuity and differntiability, limits and convergence
4) Measure theory : probability measures, absolute continuity, Markov transitions, Borel sets, abstract Measure theory
5) Dynamical systems : orbit, invariant measure. fixed points, invariant sets
Sources
[1] Homology and homotopy for arbitrary categories - S Das (foundational paper presenting the categorical version of homotopy-homology)
[2] Functors induced by comma categories - S Das (exposition on comma categories)
[3] J. Rotman. An introduction to algebraic topology, volume 119. Springer S (Algebraic topology presented in the language of category theory)
[4] Persistence Diagrams as Diagrams - A Categorification of the Stability Theorem - M Lesnick, U Bauer (topological data analysis)
[5] Simplicial Complex Representation Learning - M Hajij (topological data analysis)
[6] Dynamics, data and reconstruction - S. Das, T. Suda
[7]Dynamical systems as enriched functors - S. Das, T. Suda
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