A Note on Non-hyperbolic Fixed Points of One-Dimensional Maps

2020 ◽  
pp. 257-267
Author(s):  
Sinan Kapçak
Keyword(s):  
Fixed Points ◽  
One Dimensional ◽  
Hyperbolic Fixed Points ◽  
One Dimensional Maps

scholarly journals Gevrey estimates for one dimensional parabolic invariant manifolds of non-hyperbolic fixed points

2017 ◽  
Vol 37 (8) ◽  
pp. 4159-4190 ◽  
Author(s):  
Inmaculada Baldomá ◽  
◽  
Ernest Fontich ◽  
Pau Martín ◽  
◽  
...  
Keyword(s):  
Fixed Points ◽  
Invariant Manifolds ◽  
One Dimensional ◽  
Hyperbolic Fixed Points ◽  
Gevrey Estimates

scholarly journals Faà di Bruno's formula and nonhyperbolic fixed points of one-dimensional maps

2004 ◽  
Vol 2004 (29) ◽  
pp. 1543-1549 ◽  
Author(s):  
Vadim Ponomarenko
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Schwarzian Derivative ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Maclaurin Series ◽  
One Dimensional ◽  
One Dimensional Maps

Fixed-point theory of one-dimensional maps ofℝdoes not completely address the issue of nonhyperbolic fixed points. This note generalizes the existing tests to completely classify all such fixed points. To do this, a family of operators are exhibited that are analogous to generalizations of the Schwarzian derivative. In addition, a family of functionsfare exhibited such that the Maclaurin series off(f(x))andxare identical.

scholarly journals Stability of Hyperbolic and Nonhyperbolic Fixed Points of One-dimensional Maps

2003 ◽  
Vol 9 (5) ◽  
pp. 449-457 ◽  
Author(s):  
Fozi M. Dannan ◽  
Saber N. Elaydi ◽  
Vadim Ponomarenko
Keyword(s):  
Fixed Points ◽  
One Dimensional ◽  
One Dimensional Maps

scholarly journals On the finiteness of attractors for one-dimensional maps with discontinuities

2021 ◽  
Vol 389 ◽  
pp. 107891
Author(s):  
P. Brandão ◽  
J. Palis ◽  
V. Pinheiro
Keyword(s):  
One Dimensional ◽  
One Dimensional Maps

Discrete-Time Memristor Model for Enhancing Chaotic Complexity and Application in Secure Communication

2022 ◽  
Author(s):  
Wenhao Yan ◽  
Zijing Jiang ◽  
Qun Ding
Keyword(s):  
Fixed Points ◽  
Discrete Time ◽  
Dynamic Characteristics ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Two Dimensional ◽  
Initial State ◽  
One Dimensional ◽  
Backward Euler ◽  
Short Period

Abstract The physical implementation of continuoustime memristor makes it widely used in chaotic circuits, whereas discrete-time memristor has not received much attention. In this paper, the backward-Euler method is used to discretize TiO2 memristor model, and the discretized model also meets the three fingerprinter characteristics of the generalized memristor. The short period phenomenon and uneven output distribution of one-dimensional chaotic systems affect their applications in some fields, so it is necessary to improve the dynamic characteristics of one-dimensional chaotic systems. In this paper, a two-dimensional discrete-time memristor model is obtained by linear coupling the proposed TiO2 memristor model and one-dimensional chaotic systems. Since the two-dimensional model has infinite fixed points, the stability of these fixed points depends on the coupling parameters and the initial state of the discrete TiO2 memristor model. Furthermore, the dynamic characteristics of one-dimensional chaotic systems can be enhanced by the proposed method. Finally, we apply the generated chaotic sequence to secure communication.

scholarly journals Weighted kneading theory of one-dimensional maps with a hole

2004 ◽  
Vol 2004 (38) ◽  
pp. 2019-2038 ◽  
Author(s):  
J. Leonel Rocha ◽  
J. Sousa Ramos
Keyword(s):  
Hausdorff Dimension ◽  
Power Series ◽  
Formal Power Series ◽  
Topological Entropy ◽  
Escape Rate ◽  
One Dimensional ◽  
One Dimensional Maps ◽  
Formal Power ◽  
Kneading Theory

The purpose of this paper is to present a weighted kneading theory for one-dimensional maps with a hole. We consider extensions of the kneading theory of Milnor and Thurston to expanding discontinuous maps with a hole and introduce weights in the formal power series. This method allows us to derive techniques to compute explicitly the topological entropy, the Hausdorff dimension, and the escape rate.

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