scholarly journals A geometrical method towards first integrals for dynamical systems

1996 ◽  
Vol 37 (12) ◽  
pp. 6198-6206 ◽  
Author(s):  
Simon Labrunie ◽  
Robert Conte
Keyword(s):  
Dynamical Systems ◽  
First Integrals ◽  
Geometrical Method

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.

Symmetries, first integrals and splittability of dynamical systems

1978 ◽  
Vol 21 (7) ◽  
pp. 253-257 ◽  
Author(s):  
F. González-Gascón ◽  
F. Moreno-Insertis
Keyword(s):  
Dynamical Systems ◽  
First Integrals
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