Weinstein Conjecture
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High Quality Content by WIKIPEDIA articles! In mathematics, the Weinstein conjecture refers to a general existence problem for periodic orbits of Hamiltonian or Reeb vector flows. More specifically, the current understanding is that a regular compact contact type level set of a Hamiltonian on a symplectic manifold should carry at least one periodic orbit of the Hamiltonian flow. The conjecture is stated for any Hamiltonian on any 2n-dimensional symplectic manifold. By definition, a level set of contact type admits a contact form obtained by contracting the Hamiltonian vector field into the sym...
High Quality Content by WIKIPEDIA articles! In mathematics, the Weinstein conjecture refers to a general existence problem for periodic orbits of Hamiltonian or Reeb vector flows. More specifically, the current understanding is that a regular compact contact type level set of a Hamiltonian on a symplectic manifold should carry at least one periodic orbit of the Hamiltonian flow. The conjecture is stated for any Hamiltonian on any 2n-dimensional symplectic manifold. By definition, a level set of contact type admits a contact form obtained by contracting the Hamiltonian vector field into the symplectic form. In this case, the Hamiltonian flow is a Reeb vector field on that level set. It is a fact that any contact manifold (M, ) can be embedded into a canonical symplectic manifold, called the symplectization of M, such that M is a contact type level set (of a canonically defined Hamiltonian) and the Reeb vector field is a Hamiltonian flow.
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