Different Types of Discrete-Time and Discrete-Space Dynamical Systems

2019 ◽  
pp. 35-56
Author(s):  
Kuize Zhang ◽  
Lijun Zhang ◽  
Lihua Xie
Keyword(s):  
Dynamical Systems ◽  
Discrete Time ◽  
Discrete Space ◽  
Different Types

Discrete-Time and Discrete-Space Dynamical Systems

2020 ◽  
Author(s):  
Kuize Zhang ◽  
Lijun Zhang ◽  
Lihua Xie
Keyword(s):  
Dynamical Systems ◽  
Discrete Time ◽  
Discrete Space

CHAOTIC DYNAMICS FOR MAPS IN ONE AND TWO DIMENSIONS: A GEOMETRICAL METHOD AND APPLICATIONS TO ECONOMICS

2009 ◽  
Vol 19 (10) ◽  
pp. 3283-3309 ◽  
Author(s):  
ALFREDO MEDIO ◽  
MARINA PIREDDU ◽  
FABIO ZANOLIN
Keyword(s):  
Dynamical Systems ◽  
Discrete Time ◽  
Chaotic Dynamics ◽  
Economic Models ◽  
Two Dimensions ◽  
Geometrical Method ◽  
Mathematical Ideas ◽  
Definition Of ◽  
Applications To Economics ◽  
Discrete Time Dynamical Systems

This article describes a method — called here "the method of Stretching Along the Paths" (SAP) — to prove the existence of chaotic sets in discrete-time dynamical systems. The method of SAP, although mathematically rigorous, is based on some elementary geometrical considerations and is relatively easy to apply to models arising in applications. The paper provides a description of the basic mathematical ideas behind the method, as well as three applications to economic models. Incidentally, the paper also discusses some questions concerning the definition of chaos and some problems arising from economic models in which the dynamics are defined only implicitly.

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