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February, 2020 Time-asymptotic Dynamics of Hermitian Riccati Differential Equations
Yueh-Cheng Kuo, Huey-Er Lin, Shih-Feng Shieh
Taiwanese J. Math. 24(1): 131-158 (February, 2020). DOI: 10.11650/tjm/190605

Abstract

The matrix Riccati differential equation (RDE) raises in a wide variety of applications for science and applied mathematics. We are particularly interested in the Hermitian Riccati Differential Equation (HRDE). Radon's lemma gives a solution representation to HRDE. Although solutions of HRDE may show the finite escape time phenomenon, we can investigate the time asymptotic dynamical behavior of HRDE by its extended solutions. In this paper, we adapt the Hamiltonian Jordan canonical form to characterize the time asymptotic phenomena of the extended solutions for HRDE in four elementary cases. The extended solutions of HRDE exhibit the dynamics of heteroclinic, homoclinic and periodic orbits in the elementary cases under some conditions.

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Yueh-Cheng Kuo. Huey-Er Lin. Shih-Feng Shieh. "Time-asymptotic Dynamics of Hermitian Riccati Differential Equations." Taiwanese J. Math. 24 (1) 131 - 158, February, 2020. https://doi.org/10.11650/tjm/190605

Information

Received: 13 September 2018; Revised: 21 February 2019; Accepted: 23 June 2019; Published: February, 2020
First available in Project Euclid: 5 July 2019

zbMATH: 07175544
MathSciNet: MR4053842
Digital Object Identifier: 10.11650/tjm/190605

Subjects:
Primary: 15Axx , 31B35 , 65L20 , 93C15

Keywords: extended solutions , finite escape time phenomenon , Hamiltonian Jordan canonical form , Hermitian Riccati differential equation , Radon's lemma , Riccati differential equation

Rights: Copyright © 2020 The Mathematical Society of the Republic of China

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Vol.24 • No. 1 • February, 2020
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