Hi everyone! Let me start by sharing my background to frame what I'm looking for:

• I come from a machine learning and control theory background, and recently I've shifted my research focus to nonlinear systems.
• I'm particularly interested in rigorous mathematical analysis, stability, and control of nonlinear dynamical systems.
• I also have a strong mathematical foundation in measure theory, functional analysis, and ergodic theory.

Specifically, I'm on the hunt for references that meet two key criteria:

• Clearly introduce Lie Groups and Lie Algebras (with enough mathematical rigor matching my background)
• Provide specialized coverage of how these tools apply to nonlinear systems

I'm using the following article as my main motivation for this search:

$[1]$ Chein-Shan Liu,
A Lie-group DSO(n) method for nonlinear dynamical systems,
Applied Mathematics Letters,
Volume 26, Issue 7,
2013,
Pages 710-717,
ISSN 0893-9659,
DOI: 10.1016/j.aml.2013.01.012

备注：内容来源于stack exchange，提问作者User19212341