Generalized Dynamical Ordering and Topological Entropy in the Henon Map

2005 ◽  
Vol 114 (4) ◽  
pp. 763-791 ◽  
Author(s):  
Y. Yamaguchi ◽  
K. Tanikawa
Keyword(s):  
Topological Entropy ◽  
Hénon Map ◽  
Henon Map

On Topological Entropy of Finite Representations of the Hénon Map

2019 ◽  
Vol 29 (13) ◽  
pp. 1950175
Author(s):  
Zbigniew Galias
Keyword(s):  
Topological Entropy ◽  
Hénon Map ◽  
Henon Map

The topological entropy of finite representations of the Hénon map is studied. Efficient methods to compute the topological entropy of finite representations of maps are presented. Accurate finite representations of the Hénon map and its iterates are constructed and the topological entropy of these representations is calculated. The relation between the topological entropy of the Hénon map and the topological entropy of its finite representations is discussed.

Symbolic Dynamics and Topological Entropy of Henon Map

1991 ◽  
Vol 15 (1) ◽  
pp. 1-8
Author(s):  
Liu Wu–ming ◽  
Ying Yang–jun ◽  
Chen Shi–gang ◽  
He Xian–tu
Keyword(s):  
Topological Entropy ◽  
Symbolic Dynamics ◽  
Hénon Map ◽  
Henon Map

Autoregressive self-tuning feedback control of the Hénon map

1996 ◽  
Vol 54 (6) ◽  
pp. 6201-6206 ◽  
Author(s):  
Michael E. Brandt ◽  
Ahmet Ademoǧlu ◽  
Dejian Lai ◽  
Guanrong Chen
Keyword(s):  
Feedback Control ◽  
Hénon Map ◽  
Henon Map ◽  
Self Tuning

scholarly journals Detecting and stabilizing periodic orbits of chaotic Henon map through predictive control

2018 ◽  
Vol 27 (2018) ◽  
pp. 73-78
Author(s):  
Dumitru Deleanu
Keyword(s):  
Periodic Orbits ◽  
Predictive Control ◽  
Nonnegative Integer ◽  
Strange Attractor ◽  
Discrete System ◽  
Control Method ◽  
Nonlinear Mapping ◽  
Unstable Periodic Orbits ◽  
Hénon Map ◽  
Henon Map

The predictive control method is one of the proposed techniques based on the location and stabilization of the unstable periodic orbits (UPOs) embedded in the strange attractor of a nonlinear mapping. It assumes the addition of a small control term to the uncontrolled state of the discrete system. This term depends on the predictive state ps + 1 and p(s + 1) + 1 iterations forward, where s is the length of the UPO, and p is a large enough nonnegative integer. In this paper, extensive numerical simulations on the Henon map are carried out to confirm the ability of the predictive control to detect and stabilize all the UPOs up to a maximum length of the period. The role played by each involved parameter is investigated and additional results to those reported in the literature are presented.

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