1997/06/04 by Michael Blank, M. Blank, Tyll Krüger +6 · 6 citations
Engineering · Mathematics · Physics and Astronomy · #Applied mathematics #Calculus (dental) #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Fault Detection and Control Systems #Geology #Hamiltonian system #Kolmogorov–Arnold–Moser theorem #Mathematical analysis #Mathematical economics #Mathematics #Type (biology) #chao-dyn #nlin.CD
paper · pdf · doi:10.48550/arxiv.chao-dyn/9706005
published in arXiv (Cornell University) (Cornell University) · 9 pages, LaTeX (1 figure is available upon request)
arxiv created 1997/06/04 · openalex publication_date 1997/06/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Perturbations due to round-off errors in computer modeling are discontinuous and therefore one cannot use results like KAM theory about smooth perturbations of twist maps. We elaborate a special approximation scheme to construct two smooth periodic on the angle perturbations of the twist map, bounding the discretized map from above and from below. Using the well known Moser's theorem we prove the existence of invariant curves for these smooth approximations. As a result we are able to prove that any trajectory of the discretized twist map is eventually periodic. We discuss also some questions, concerning the application of the intersection property in Moser's theorem and the generalization of our results for the twist map in Lobachevski plane.