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Abstract <p>The paper examines high-order asymptotic formulas for eigenvalue perturbations of Hamiltonian matrices dependent on a small parameter. A procedure for constructing such formulas in principal cases is proposed. New stability criteria for autonomous Hamiltonian systems at small parameter values are developed. Examples of applying the obtained results for stability analysis of linear systems are provided.</p>

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High-order Asymptotic Formulas for Perturbations of Eigenvalues of Hamiltonian Matrices

  • 期刊论文

  • 发表日期：

    2025年7月1日

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  • M. G. Yumagulov,
  • A. S. Belova

摘要

Abstract

The paper examines high-order asymptotic formulas for eigenvalue perturbations of Hamiltonian matrices dependent on a small parameter. A procedure for constructing such formulas in principal cases is proposed. New stability criteria for autonomous Hamiltonian systems at small parameter values are developed. Examples of applying the obtained results for stability analysis of linear systems are provided.