# Approximation Dynamics

## TL;DR

This paper presents methods for approximating complex continuous dynamical systems on manifolds and Cantor sets using simpler, tractable systems with finite ergodic components, facilitating analysis and understanding.

## Contribution

It introduces a novel approach to approximate continuous dynamical systems with finite chain components on p. l. manifolds and Cantor sets using simplicial and shift-like systems.

## Key findings

- Effective approximation of continuous systems by tractable models
- Finite ergodic decomposition for almost all points
- Applicability to p. l. manifolds and Cantor sets

## Abstract

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.

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Source: https://tomesphere.com/paper/1702.02596