Conservative chaos in a simple oscillatory system with non-smooth nonlinearity

In this paper, we consider some unusual features of dynamical regimes in the non-smooth potential V(x)=|x|\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V(x)=|x|$$\end{document} which is a piece-wise linear function. Also, we consider the dynamics in more complicated potential V(x)=|x|-a\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V(x)=\left| |x|-a\right| $$\end{document} which is quite similar to the well-known double-well potential within the Duffing model. Numerical results for Poincaré sections, bifurcation diagrams, and Lyapunov spectra together with dependencies of the largest Lyapunov characteristic exponent on the parameters of the excitation force are also obtained and analyzed. A comparison of the proposed systems and the Duffing model with the same fixed points is also done. Our numerical results show that such a relatively simple oscillatory system has rich nonlinear dynamics and exhibits a conservative character of chaos. This makes it possible to consider these systems as promising sources of chaotic signals in the field of modern chaos-based information technologies and digital communications.