Break-up of invariant curves in the Fermi-Ulam model. (September 2022)

• Record Type: Journal Article
• Authors: Hermes, Joelson D.V.; dos Reis, Marcelo A.; Caldas, Iberê L.; Leonel, Edson D.
• Is Part Of: Chaos, solitons and fractals. Volume 162(2022)
• Publication Date: 2022-09
• Subjects: Chaos -- Nonlinear dynamics -- Mappings -- Hamiltonian systems; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2022.112410
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: The transport of particles in the phase space is investigated in the Fermi-Ulam model. The system consists of a particle confined to move within two rigid walls with which it collides. One is fixed and the other is periodically moving in time. In this work we investigate, for this model, the location of invariant curves that separate chaotic areas in the phase space. Applying the Slater's theorem we verify that the mapping presents a family of invariant spanning curves with a rotation number whose expansion into continued fractions has an infinite tail of the unity, acting as local transport barriers. We study the destruction of such curves and find the critical parameters for that. The determination of the rotation number in the vicinity of one of the considered spanning curves allowed us to understand the dynamics in the vicinity of the considered curve, both before and after criticality. The rotation number profile showed us the fractal character of the region close to the curve, since this profile has a structure similar to a "Devil's Staircase". Highlights: We investigate the location of invariant curves for the Fermi-Ulam model that separate chaotic areas in phase space. We found, for this model, a family of quite robust invariant spanning curves. Through Slater's theorem, we find the position of a family of locally robust invariant spanning curves. Using Slater's theorem allowed us to study the criticality for each of these curves. We determined the critical parameter related to each curve and thus we were able to predict their breakage. We show a similar structure to "Devil's Staircase" for the rotation number profile in the vicinity of the curves.