# Universal Exponent for Transport in Mixed Hamiltonian Dynamics

## TL;DR

This paper demonstrates that a Markov model accurately predicts universal transport properties in mixed Hamiltonian systems, revealing a consistent power-law decay exponent across different maps.

## Contribution

It introduces a universal Markov model for transport in mixed phase space and confirms its predictions with numerical simulations.

## Key findings

- Survival probability decays as a power law with exponent 1.57
- Universal distributions match simulations of Hénon and Chirikov-Taylor maps
- Supports the Meiss-Ott Markov tree model for mixed systems

## Abstract

We compute universal distributions for the transition probabilities of a Markov model for transport in the mixed phase space of area-preserving maps and verify that the survival probability distribution for trajectories near an infinite island-around-island hierarchy exhibits, on average, a power law decay with exponent $\gamma = 1.57$. This exponent agrees with that found from simulations of the H\'enon and Chirikov-Taylor maps. This provides evidence that the Meiss-Ott Markov tree model describes the transport for mixed systems.