On exponentially accurate approximation of a near the identity map by an autonomous flow

TL;DR

This paper proves that an analytic near-identity map can be approximated by an autonomous flow with exponential accuracy, providing explicit formulas and error bounds, refining Neishtadt's theorem.

Contribution

It offers a refined proof of Neishtadt's theorem with explicit vector field expressions and error bounds for exponential approximation of near-identity maps.

Findings

Exponential accuracy in approximation of near-identity maps by autonomous flows

Explicit formulas for vector fields used in approximation

Quantitative bounds on approximation errors

Abstract

This paper contains a proof of a refined version of Neishtadt's theorem which states that an analytic near-identity map can be approximated by the time-one map of an autonomous flow with exponential accuracy. We provide explicit expressions for the vector fields and give explicit bounds for the error terms.