A Hamiltonian system is a dynamical system governed by Hamilton's equations. In physics, this dynamical system describes the evolution of a physical system...

sufficiently large time. Many systems studied in physics are completely integrable, in particular, in the Hamiltonian sense, the key example being multi-dimensional...

physics, Hamiltonian mechanics is a reformulation of Lagrangian mechanics that emerged in 1833. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics...

In mathematics, a superintegrable Hamiltonian system is a Hamiltonian system on a 2 n {\displaystyle 2n} -dimensional symplectic manifold for which the...

a first-class constraint is a dynamical quantity in a constrained Hamiltonian system whose Poisson bracket with all the other constraints vanishes on the...

of a system Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system Dyall Hamiltonian, a modified Hamiltonian with...

the measures supported on periodic orbits of the Hamiltonian system. For chaotic dissipative systems the choice of invariant measure is technically more...

statistical and Hamiltonian mechanics. It asserts that the phase-space distribution function is constant along the trajectories of the system—that is that...

(x,y).} Hénon–Heiles system shows rich dynamical behavior. Usually the Wada property cannot be seen in the Hamiltonian system, but Hénon–Heiles exit...

of trajectories in phase space of an integrable Hamiltonian system. The motion of an integrable system is confined to an invariant torus (a doughnut-shaped...

theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycle (or...

In quantum mechanics, the Hamiltonian of a system is an operator corresponding to the total energy of that system, including both kinetic energy and potential...

The Hamiltonian is a function used to solve a problem of optimal control for a dynamical system. It can be understood as an instantaneous increment of...

In dynamical systems theory, the Liouville–Arnold theorem states that if, in a Hamiltonian dynamical system with n degrees of freedom, there are also n...

solve the so-called Hamiltonian system, which is a two-point boundary value problem, plus a maximum condition of the control Hamiltonian. These necessary...

Hamilton (1769–1829) was an Irish language teacher, who introduced the "Hamiltonian system" of teaching languages. Hamilton was taught for four years at a Dublin...

between gauge invariance and "BRST invariance" forces the choice of a Hamiltonian system whose states are composed of "particles" according to the rules familiar...

eigenvalues (energy levels) with the classical behavior of the same Hamiltonian (system). Study of probability distribution of individual eigenstates (see...

object in a given Hamiltonian system, the quantum butterfly effect considers the effect of a small change in the Hamiltonian system with a given initial...

over a long period of time. Liouville's theorem states that, for a Hamiltonian system, the local density of microstates following a particle path through...

\displaystyle y^{\prime \prime }=2y^{3}+ty+b-1/2} is equivalent to the Hamiltonian system q ′ = ∂ H ∂ p = p − q 2 − t / 2 {\displaystyle \displaystyle q^{\prime...

The Hamiltonian path problem is a topic discussed in the fields of complexity theory and graph theory. It decides if a directed or undirected graph, G...

abstractly by Hamiltonian mechanics or Lagrangian mechanics. The concept of time evolution may be applicable to other stateful systems as well. For instance...

diffusion is the phenomenon of instability of nearly-integrable Hamiltonian systems. The phenomenon is named after Vladimir Arnold who was the first...

from it without loss of speed (i.e. elastic collisions). Billiards are Hamiltonian idealizations of the game of billiards, but where the region contained...

quantum systems. Hamiltonian simulation is a problem that demands algorithms which implement the evolution of a quantum state efficiently. The Hamiltonian simulation...

dissipative Kuramoto model is contained in certain conservative Hamiltonian systems with Hamiltonian of the form H ( q 1 , … , q N , p 1 , … , p N ) = ∑ i = 1...

within condensed-matter physics, a gapped Hamiltonian is a Hamiltonian for an infinitely large many-body system where there is a finite energy gap separating...

Hamiltonian fluid mechanics is the application of Hamiltonian methods to fluid mechanics. Note that this formalism only applies to non-dissipative fluids...

the studied systems. In 1959 Boris Valerianovich Chirikov proposed a criterion for the emergence of classical chaos in Hamiltonian systems (Chirikov criterion)...