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.

Medio, A., Pireddu, M., Zanolin, F. (2009). Chaotic dynamics for maps in one and two dimensions: A geometrical method and applications to economics. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS IN APPLIED SCIENCES AND ENGINEERING, 19, 3283-3309 [10.1142/S0218127409024761].

Chaotic dynamics for maps in one and two dimensions: A geometrical method and applications to economics

PIREDDU, MARINA;
2009

Abstract

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.
Articolo in rivista - Articolo scientifico
Chaotic dynamics; SAP; discrete-time dynamical systems
English
2009
19
3283
3309
none
Medio, A., Pireddu, M., Zanolin, F. (2009). Chaotic dynamics for maps in one and two dimensions: A geometrical method and applications to economics. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS IN APPLIED SCIENCES AND ENGINEERING, 19, 3283-3309 [10.1142/S0218127409024761].
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/46083
Citazioni
  • Scopus 50
  • ???jsp.display-item.citation.isi??? 44
Social impact