Two Layer Model via Non Quasi Periodic Normal Form Theory

TL;DR

This paper applies a non quasi periodic normal form theory to a two layer dynamical system, providing explicit estimates of resonance trapping times that are exponentially long relative to system parameters.

Contribution

It introduces a non quasi periodic normal form approach to analyze resonance trapping in a two layer model, offering explicit exponential estimates for trapping durations.

Findings

Resonance trapping time is exponentially long in small parameters.

The model is reformulated using a non quasi periodic normal form.

Explicit estimates for resonance trapping duration are derived.

Abstract

The two layer model is a 2+1/2 degrees of freedom non autonomous dynamical system whose lower order expansion exhibits capture in resonance, numerically detected in a previous paper by the authors. In this paper, we reframe the model along the lines of a suitable version of (which we refer to as non quasi periodic) normal form theory and provide an explicit amount of the resonance trapping time, which is estimated as exponentially long, in terms of the small parameters of the system. Key words: capture into resonance; non quasi periodic normal form theory; friction. MSC 2020: 37J40; 70F40.