Discrete differential manifolds and dynamics on networks | Zendy

Aristophanes Dimakis | Zendy; Folkert Müller-Hoissen | Zendy; F. Vanderseypen | Zendy

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Discrete differential manifolds and dynamics on networks

Author(s) -

Aristophanes Dimakis,

Folkert Müller-Hoissen,

F. Vanderseypen

Publication year - 1995

Publication title -

journal of mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.708

H-Index - 119

eISSN - 1089-7658

pISSN - 0022-2488

DOI - 10.1063/1.530996

Subject(s) - differentiable function , mathematics , differential topology , manifold (fluid mechanics) , differential (mechanical device) , countable set , dynamical systems theory , pure mathematics , space (punctuation) , differential geometry , topology (electrical circuits) , computer science , geometry , ricci flat manifold , combinatorics , physics , mechanical engineering , scalar curvature , curvature , quantum mechanics , engineering , aerospace engineering , operating system

A `discrete differential manifold' we call a countable set together with analgebraic differential calculus on it. This structure has already been exploredin previous work and provides us with a convenient framework for theformulation of dynamical models on networks and physical theories with discretespace and time. We present several examples and introduce a notion ofdifferentiability of maps between discrete differential manifolds. Particularattention is given to differentiable curves in such spaces. Every discretedifferentiable manifold carries a topology and we show that differentiabilityof a map implies continuity.Comment: 26 pages, LaTeX (RevTex), GOET-TP 88/9

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