Deterministic chaos for Markov chains
Marat Akhmet
TL;DR
This paper demonstrates that finite-state Markov chains exhibit Poincare chaos, with finite realizations forming parts of unpredictable orbits, supported by numerical simulations.
Contribution
It establishes that finite Markov chains are inherently Poincare chaotic and provides illustrative numerical examples.
Findings
Finite Markov chains are Poincare chaotic.
Finite realizations are segments of unpredictable orbits.
Numerical simulations support theoretical results.
Abstract
We find that Markov chains with finite state space are Poincare chaotic. Moreover, finite realizations of the chains are arcs of each unpredictable orbit for sure. An illustrating example with a proper numerical simulation is provided.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical Dynamics and Fractals · Quantum chaos and dynamical systems · Chaos control and synchronization