A topological approach to the problem of chaotic tides. (December 2022)

• Record Type: Journal Article
• Authors: Burra, Lakshmi; Zanolin, Fabio
• Is Part Of: Nonlinear analysis. Volume 68(2022)
• Publication Date: 2022-12
• Subjects: Nonautonomous Duffing equations -- Poincaré map -- Subharmonic solutions -- Topological horseshoes -- Chaotic dynamics -- Tides; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103699
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We study the existence of subharmonic solutions and solutions with complicated dynamics in a Duffing-type equation which arises from the study of forced tides. This is a model which involves an almost enclosed basin, connected to the sea by a narrow strait. Such a basin turns out to be a nonlinear Helmholtz resonator. The proofs are based on developments of the theory of topological horseshoes in connection with some geometric features associated to linked twist maps.