Dynamics of Sawtooth Map: 1. New Numerical Results
Vitold V. Vecheslavov
Abstract
Some results of numerical study of the canonical map with a sawtooth force are given and discovered new unexpected dynamical effects are described. In particular, it is shown that if the values of the system parameter K belong to the countable set determined by Ovsyannikov's theorem, separatrices of primary resonances are not splitted and chaotic layers are not formed. One more set of values of the parameter related to the other family of nondestructed separatrices of primary resonances was found. The mechanism explaining the stability of the primary resonance separatrix in the critical regime is found and described. First secondary resonances were studies and for them were found the K-values at which their separatrices are not splitted also. New problems and open questions occurred in this connections whose solution can facilitate the further development of the nonlinear Hamiltonian systems theory are presented.
Create a lesson
Related papers
A comparison of three models of a whirling string as it becomes chaotic
Nicholas B. Tufillaro
Modal interactions in strongly nonlinear coupled oscillators with closely spaced modes and nonclassical damping distribution
C. A. Hubay, T. Kalmar-Nagy, L. Bergman et al.
Nonintegrability theorem on perturbed integrable Hamiltonian dynamical systems with two independent resonances
Nikos Zafeiriadis, Efthymia Meletlidou, Christos Efthymiopoulos et al.
PRISM: Unifying multiphysics optothermal transport and identifiability-guided inference for nanoscale thermal metrology
Yicong Qiu, Ziyang Zhong, Ziyan Qian et al.
Ultraslow diffusion emerging from local symmetry breaking in quenched disorder
Jin Liu, Rainer Klages, Huihai Wang et al.
A model for the dimension of the inertial manifold of the Kuramoto-Sivashinsky equation
Melisa Y. Vinograd, Patricio Clark di Leoni