In the context of physical systems, dynamical systems are mathematical models that describe the time evolution of a system’s state, typically represented as points in a phase space governed by deterministic laws such as ordinary or partial differential equations, or discrete maps. Physical dynamical systems encode conservation laws, symmetries, and constraints arising from mechanics, electromagnetism, or other fundamental interactions. Their trajectories can exhibit fixed points, limit cycles, and chaotic attractors, with stability properties analyzed via linearization, Lyapunov exponents, and invariant manifolds. Dynamical systems theory provides a rigorous framework for predicting and characterizing the temporal behavior of physical systems across scales.
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