2025/03/26 by Laura Gardini, Gardini, Laura, Davide Radi +7
Mathematics · Economics, Econometrics and Finance · #Mathematical Dynamics and Fractals #Complex Systems and Time Series Analysis #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2503.20449
Piecewise smooth systems are intensively studied today in many application areas, such as economics, finance, engineering, biology, and ecology. In this work, we consider a class of one-dimensional piecewise linear discontinuous maps with a finite number of partitions and functions sharing the same real fixed point. We show that the dynamics of this class of maps can be analyzed using the well-known piecewise linear circle map and prove that their bounded behavior, unrelated to the fixed point, may consist of either nonhyperbolic cycles or quasiperiodic orbits densely filling certain segments, with possible coexistence. A corresponding model describing the price dynamics of a financial market serves as an illustrative example. While simulated model dynamics may be mistaken for chaotic behavior, our results demonstrate that they are quasiperiodic.