Partial linearization for nonautonomous differential equations
Xia Pan, Zuohuan Zheng
TL;DR
This paper establishes conditions under which nonautonomous differential equations can be partially linearized, using the dichotomy spectrum to extend linearization techniques to more complex, time-dependent systems.
Contribution
It introduces a novel partial linearization method for n-dimensional nonautonomous differential equations based on the dichotomy spectrum.
Findings
Proves partial linearization under new spectral conditions
Extends linearization theory to nonautonomous systems
Provides a framework for analyzing complex time-dependent dynamics
Abstract
In this paper, we prove the partial linearization for n-dimensional nonautonomous differential equations. The conditions are formulated in terms of the dichotomy spectrum.
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Taxonomy
TopicsStability and Controllability of Differential Equations · Numerical methods for differential equations · Advanced Mathematical Modeling in Engineering