scholarly journals Convergence speed of a Ruelle operator associated with a non-uniformly expanding conformal dynamical system and a Dini potential

2018 ◽  
Vol 38 (9) ◽  
pp. 4693-4713 ◽  
Author(s):  
Yunping Jiang ◽  
◽  
Yuan-Ling Ye ◽  
◽  
Keyword(s):  
Dynamical System ◽  
Convergence Speed ◽  
Ruelle Operator

Decay of correlations for weakly expanding dynamical systems with Dini potentials under optimal quasi-gap condition

Nonlinearity ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 916-953
Author(s):  
Yunping Jiang ◽  
Yuan-Ling Ye
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Decay Of Correlations ◽  
Ruelle Operator

Abstract We find an optimal quasi-gap condition for a weakly expanding dynamical system associated with Dini potential. Under this optimal quasi-gap condition, we prove the Ruelle operator theorem and further the decay of the correlations for any weakly expanding dynamical systems with Dini potentials.

scholarly journals Convergence Speed of a Dynamical System for Sparse Recovery

2013 ◽  
Vol 61 (17) ◽  
pp. 4259-4269 ◽  
Author(s):  
Aurele Balavoine ◽  
Christopher J. Rozell ◽  
Justin Romberg
Keyword(s):  
Dynamical System ◽  
Sparse Recovery ◽  
Convergence Speed

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.

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