Smale Horseshoe in a Piecewise Smooth Map

Release time:2019-07-11

Journal:INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS

Place of Publication:WORLD SCIENTIFIC PUBL CO PTE LTD, 5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE

Key Words:Impact oscillator; Nordmark map; nonwandering set; Smale horseshoe

Abstract:We investigate the chaotic dynamics of a two-dimensional piecewise smooth map. The map represents the normal form of a discrete time representation of impact oscillators near grazing states. It is proved that, in certain region of the parameter space, the nonwandering set of the map is contained in a bounded region and that, restricted to the nonwandering set, the map is topologically conjugate to the two-sided shift map on two symbols.

Co-author:Xie Jianhua

First Author:Li Denghui

Indexed by:Unit Twenty Basic Research

Correspondence Author:Chen Hebai*

Document Code:10.1142/S0218127419500512

Document Type:J

Volume:29

Issue:4

Page Number:1950051

ISSN No.:0218-1274

Translation or Not:no

Date of Publication:2019-04-01