On the shifts of orbits and periodic orbits under perturbation and the change of Poincaré map Jacobian of periodic orbits

Fuente: arXiv
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Auteurs principaux: Wei, Wenyin, Knieps, Alexander, Liang, Yunfeng
Format: Preprint
Publié: 2024
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author Wei, Wenyin
Knieps, Alexander
Liang, Yunfeng
author_facet Wei, Wenyin
Knieps, Alexander
Liang, Yunfeng
contents Periodic orbits and cycles, respectively, play a significant role in discrete- and continuous-time dynamical systems (i.e. maps and flows). To succinctly describe their shifts when the system is applied perturbation, the notions of functional and functional derivative are borrowed from functional analysis to consider the whole system as an argument of the geometric representation of the periodic orbit or cycle. The shifts of an orbit/trajectory and periodic orbit/cycle are analyzed and concluded as formulae for maps/flows, respectively. The theory shall be beneficial for analyzing sensitivity to perturbations, and optimizing and controlling various systems.
format Preprint
id arxiv_https___arxiv_org_abs_2407_08079
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On the shifts of orbits and periodic orbits under perturbation and the change of Poincaré map Jacobian of periodic orbits
Wei, Wenyin
Knieps, Alexander
Liang, Yunfeng
Dynamical Systems
Functional Analysis
Optimization and Control
Chaotic Dynamics
Plasma Physics
Primary: 34D10 Secondary: 37D10, 37N05, 37N10, 37M21, 37J40, 37J46, 39A33, 39B52, 76W05, 78M30
Periodic orbits and cycles, respectively, play a significant role in discrete- and continuous-time dynamical systems (i.e. maps and flows). To succinctly describe their shifts when the system is applied perturbation, the notions of functional and functional derivative are borrowed from functional analysis to consider the whole system as an argument of the geometric representation of the periodic orbit or cycle. The shifts of an orbit/trajectory and periodic orbit/cycle are analyzed and concluded as formulae for maps/flows, respectively. The theory shall be beneficial for analyzing sensitivity to perturbations, and optimizing and controlling various systems.
title On the shifts of orbits and periodic orbits under perturbation and the change of Poincaré map Jacobian of periodic orbits
topic Dynamical Systems
Functional Analysis
Optimization and Control
Chaotic Dynamics
Plasma Physics
Primary: 34D10 Secondary: 37D10, 37N05, 37N10, 37M21, 37J40, 37J46, 39A33, 39B52, 76W05, 78M30
url https://arxiv.org/abs/2407.08079