Non-Integrable Dynamics and Physics Beyond the Standard Model

Abstract

The evolution of integrable classical systems leads to conserved quantities and vanishing Poisson brackets. In contrast, such invariants do not exist in the dynamics of non-integrable systems, which include (but are not limited to) deterministic models with long-term chaotic behavior. The object of this review is to briefly survey the mathematical background of nonintegrability and its role in the physics unfolding well-above the Standard Model (SM) scale.