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Dynamical systems theory Ergodic theory Cantor set Mathematics Dynamical system (definition) Invariant (physics) Invariant measure Measure (data warehouse) Degenerate energy levels Finite set Cantor function Measure-preserving dynamical system Pure mathematics Null set Manifold (fluid mechanics) Cantor's diagonal argument Set (abstract data type) Linear dynamical system Random dynamical system Mathematical analysis Computer science Physics Mathematical physics Linear system Quantum mechanics Database Mechanical engineering Programming language Engineering

Ethan Akin ·

YOU? · · 2017 · Open Access · · DOI: https://doi.org/10.48550/arxiv.1702.02596 · OA: W2947755667

We describe the approximation of a continuous dynamical system on a p. l. manifold or Cantor set by a tractable system. A system is tractable when it has a finite number of chain components and, with respect to a given full background measure, almost every point is generic for one of a finite number of ergodic invariant measures. The approximations use non-degenerate simplicial dynamical systems for p. l. manifolds and shift-like dynamical systems for Cantor Sets.

Keywords: Dynamical systems theory · Ergodic theory · Cantor set · Mathematics · Dynamical system (definition) · Invariant (physics) · Invariant measure · Measure (data warehouse) · Degenerate energy levels · Finite set · Cantor function · Measure-preserving dynamical system · Pure mathematics · Null set · Manifold (fluid mechanics) · Cantor's diagonal argument · Set (abstract data type) · Linear dynamical system · Random dynamical system · Mathematical analysis · Computer science · Physics · Mathematical physics · Linear system