Number Theory Meets Dynamics: Driven Oscillators with 2-Adic Valuation Forcing
0Day 3 | 4:00 PM–4:30 PM
"Number Theory Meets Dynamics: Driven Oscillators with 2-Adic Valuation Forcing"
Presented by:
Maila Hallare, United States Air Force Academy, USAFA CO USA
https://qubeshub.org/community/groups/simiode/expo/2025
Abstract: This presentation investigates the intriguing interplay between number theory and dynamical systems through the lens of a second-order linear differential equation forced by a 2-adic valuation on time. The 2-adic valuation measures the largest power of 2 that divides a given integer n; it is part of the larger family of p-adic valuations and plays a fundamental role in number theory. Using some elementary ideas (Laplace transforms and variation of parameters), we explore how such a number-theoretic function manifests in the system's dynamic responses. The results reveal complex, non-periodic, non-quasi-periodic behaviors characterized by intricate, piecewise oscillatory patterns. This work demonstrates the potential of number-theoretic constructs to generate novel dynamical behaviors, distinct from those produced by traditional nonhomogeneous forcing terms based on elementary functions.