A limit theorem for sojourns near indifferent fixed points of 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.

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

The Journal of Difference Equations and Applications ◽

10.1080/1023619031000078315 ◽

2003 ◽

Vol 9 (5) ◽

pp. 449-457 ◽

Cited By ~ 17

Author(s):

Fozi M. Dannan ◽

Saber N. Elaydi ◽

Vadim Ponomarenko

Keyword(s):

Fixed Points ◽

One Dimensional ◽

One Dimensional Maps

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

Advances in Mathematics ◽

10.1016/j.aim.2021.107891 ◽

2021 ◽

Vol 389 ◽

pp. 107891

Author(s):

P. Brandão ◽

J. Palis ◽

V. Pinheiro

Keyword(s):

One Dimensional ◽

One Dimensional Maps

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Total progeny in a multitype critical age dependent branching process with immigration

Journal of Applied Probability ◽

10.2307/3212690 ◽

1974 ◽

Vol 11 (3) ◽

pp. 458-470 ◽

Cited By ~ 2

Author(s):

Howard J. Weiner

Keyword(s):

Limit Theorem ◽

Branching Process ◽

Cell Types ◽

Dimensional Case ◽

One Dimensional ◽

Age Dependent ◽

Total Progeny ◽

Critical Age ◽

The One ◽

Branching Process With Immigration

In a multitype critical age dependent branching process with immigration, the numbers of cell types born by t, divided by t2, tends in law to a one-dimensional (degenerate) law whose Laplace transform is explicitily given. The method of proof makes a correspondence between the moments in the m-dimensional case and the one-dimensional case, for which the corresponding limit theorem is known. Other applications are given, a possible relaxation of moment assumptions, and extensions are indicated.

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

10.21203/rs.3.rs-1214130/v1 ◽

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.

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