# Conditional Lyapunov Exponent Criteria in terms of Ergodic Theory

## TL;DR

This paper derives a formula for the conditional Lyapunov exponent using ergodic theory, enhancing understanding of chaos synchronization phenomena.

## Contribution

It introduces a new ergodic theory-based formula for the conditional Lyapunov exponent, clarifying factors influencing chaos synchronization.

## Key findings

- Formula expressing the conditional Lyapunov exponent in ergodic terms
- Identification of factors characterizing the exponent in chaotic systems
- Enhanced theoretical understanding of chaos synchronization mechanisms

## Abstract

The conditional Lyapunov exponent is defined for investigating chaotic synchronization, in particular complete synchronization and generalized synchronization. We find that the conditional Lyapunov exponent is expressed as a formula in terms of ergodic theory. Dealing with this formula, we find what factors characterize the conditional Lyapunov exponent in chaotic systems.