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Contact Hamiltonian systems play a role a role in string theory, more specifically in what is known as the AdS-CFT correspondence. See, for example, Transverse Kähler–Ricci Solitons of Five-Dimensiona …

The gravitational or Coulomb potential has a "hidden" symmetry (hidden in the sense that it does not follow from the rotational symmetry). The resulting integral of the motion (the Runge-Lenz vector) …

The Fourier transformed density $f(\mathbf{k},t)$ plays a central in dynamic light scattering. The classic text is by Berne and Pecora (B&P). The correlator $$F(\mathbf{k},t)=\langle f(-\mathbf{k},0)f …

The Poincaré-von Zeipel method in celestial mechanics relies on canonical transformations of the Hamiltonian to separate fast and slow degrees of freedom in a solar system. See, for example, A note on …

The master thesis Nonholonomic Dynamical Systems by Brett Ryland contains several examples of non-Hamiltonian systems from classical physics: the dynamics of a laser and the evolution of a gas flame ( …

There is a great variety of methods to obtain conservation laws of nonlinear evolution equations. In a broad classification one can divide these in symmetry-based approaches (Noether's theorem relate …

In response to (1), a key advantage of Hamilton's equations of motion is that they remain invariant under a large class of "canonical" transformations, $(x,p)\mapsto (Q(x,p),P(x,p))$ for some scalar f …

Since the question is about physical implications of Poincaré recurrence one should take both quantum effects and gravitational effects into consideration. Quantum mechanics does not spoil the recurre …

The usual way to ensure the convergence of the steepest descent formulation of the Euler-Lagrange equations, is to introduce a friction term, see The Calculus of Variations by Jeff Calder. Instead of …