Trajectories of a dynamical system determined by a one-parameter group of conformal mappings of R3

1983 ◽  
Vol 24 (1) ◽  
pp. 52-56 ◽  
Author(s):  
V. P. Golubyatnikov ◽  
L. N. Pestov
Keyword(s):  
Dynamical System ◽  
Conformal Mappings ◽  
Parameter Group

Smooth derivations on abelian C*-dynamical systems

1987 ◽  
Vol 42 (2) ◽  
pp. 247-264 ◽  
Author(s):  
Derek W. Robinson
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Parameter Group ◽  
Group Of Automorphisms ◽  
Lipschitz Algebra ◽  
Image Position

AbstractLet (A, R, σ) be an abelian C*-dynamical system. Denote the generator of σ by δ0 and define A∞ = ∩n>1D (δ0n). Further define the Lipschitz algebra .If δ is a *-derivation from A∞ into A½, then it follows that δ is closable, and its closure generates a strongly continuous one-parameter group of *-automorphisms of A. Related results for local dissipations are also discussed.

On the Harmonic Oscillations for the Motion of a Dynamical System

2017 ◽  
Vol 13 (2) ◽  
pp. 4657-4670
Author(s):  
W. S. Amer
Keyword(s):  
Dynamical System ◽  
Numerical Solutions ◽  
Equation Of Motion ◽  
Parameter Method ◽  
Kutta Method ◽  
Small Parameter Method ◽  
Harmonic Oscillations ◽  
Pivot Point ◽  
Runge Kutta Method ◽  
High Consistency

This work touches two important cases for the motion of a pendulum called Sub and Ultra-harmonic cases. The small parameter method is used to obtain the approximate analytic periodic solutions of the equation of motion when the pivot point of the pendulum moves in an elliptic path. Moreover, the fourth order Runge-Kutta method is used to investigate the numerical solutions of the considered model. The comparison between both the analytical solution and the numerical ones shows high consistency between them.

Prediction of Solutions of the Duffing System with Tuned Mass Damper

2020 ◽  
Vol 22 (4) ◽  
pp. 983-990
Author(s):  
Konrad Mnich
Keyword(s):  
Dynamical System ◽  
Duffing Oscillator ◽  
Probabilistic Approach ◽  
Nonlinear Dynamical System ◽  
Tuned Mass Damper ◽  
Nonlinear Dynamical ◽  
Duffing System ◽  
Mass Damper ◽  
Basin Stability ◽  
Stability Concept

AbstractIn this work we analyze the behavior of a nonlinear dynamical system using a probabilistic approach. We focus on the coexistence of solutions and we check how the changes in the parameters of excitation influence the dynamics of the system. For the demonstration we use the Duffing oscillator with the tuned mass absorber. We mention the numerous attractors present in such a system and describe how they were found with the method based on the basin stability concept.

Sign in / Sign up

Export Citation Format

Share Document