Invariance principle in dynamical systems
Karina Marin, Mauricio Poletti
TL;DR
This survey explains the Invariance Principle in dynamical systems, detailing its foundational concepts, key results, and applications related to measure disintegration and holonomies.
Contribution
It provides a comprehensive overview of the Invariance Principle, clarifying definitions, results, and practical uses in the study of dynamical systems.
Findings
Disintegration of measures with zero center Lyapunov exponents admits extra invariance.
The survey clarifies the basic ideas and definitions behind the Invariance Principle.
Applications demonstrate how the principle is used in dynamical systems analysis.
Abstract
In this survey we talk about what is known as Invariance Principle in dynamical systems. It states that the disintegration of measures with zero center Lyapunov exponents admits some extra invariance by holonomies. We focus on explaining the basic definitions and ideas behind a series of results about the Invariance Principle and give some basic applications on how this is used in dynamical systems.
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