Discrete Differential Manifolds and Dynamics on Networks

Details Discrete Differential Manifolds and Dynamics on Networks Discrete Differential Manifolds and Dynamics on Networks

1994-08-21

arxiv.org/abs/hep-th/9408114v1

J.Math.Phys. 36 (1995) 3771-3791

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, LaTeX (RevTex), GOET-TP 88/94

Scientific paper

10.1063/1.530996

A `discrete differential manifold' we call a countable set together with an algebraic differential calculus on it. This structure has already been explored in previous work and provides us with a convenient framework for the formulation of dynamical models on networks and physical theories with discrete space and time. We present several examples and introduce a notion of differentiability of maps between discrete differential manifolds. Particular attention is given to differentiable curves in such spaces. Every discrete differentiable manifold carries a topology and we show that differentiability of a map implies continuity.

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