Generic phase transitions and profit singularities in Arnold's model

• Type: Article in International Scientific Journal
• Date: 2007

Authors

Davydov, AA (Author) Other; Mena M Matos (Author) FCUP

Journal

Title: Sbornik Mathematics

Vol. 198

Pages: 17-37

ISSN: 1064-5616

Publisher: Turpion Ltd

Indexing

ISI Web of Knowledge - 10 Citations

Scopus - 12 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-004-EK0

DOI: 10.1070/sm2007v198n01abeh003827

Abstract (EN): For a smooth one-parameter family of pairs of control systems and profit densities on a circle, the generic transitions between optimal rotations and stationary strategies are studied in the problem of maximization of the time-averaged profit on the infinite horizon. It is shown that there are only two types of such transitions, the corresponding singularities of the average profit as a function of the family parameter are found, and it is proved that these singularities are stable under small perturbations of a generic family. The classification of singularities of the maximum average profit is completed for generic families.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 21