Rigorous bounds on Lyapunov exponents of linked twist maps. (1st March 2023)

• Record Type: Journal Article
• Authors: Wright, Patrick; Niesen, Jitse; Sturman, Rob
• Is Part Of: Nonlinearity. Volume 36:Number 3(2023)
• Page Start: 1699
• Page End: 1715
• Publication Date: 2023-03-01
• Subjects: Lyapunov exponents -- return time partition -- non-uniform hyperbolicity -- invariant cones; 37A05; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/acb397
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: Rigorous, elementary upper and lower bounds upon the Lyapunov exponents of a parametrised family of linked twist maps are given, and obtained explicitly for a specific range of parameter values. The method used to obtain the bounds utilises the existence of invariant cones for specific products of the underlying family of shear maps, and the return time partition of the overlap region of the two annuli. Improvements upon the accuracy of this method are then obtained by considering preceding sequences of matrices on the orbits.