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O que (quem) é symplectic operator - definição

Symplectic transformation; Symplectic operator

Symplectic matrix

In mathematics, a symplectic matrix is a 2n\times 2n matrix M with real entries that satisfies the condition

https://en.wikipedia.org/wiki/Symplectic_matrix

Symplectic geometry

BRANCH OF DIFFERENTIAL GEOMETRY AND DIFFERENTIAL TOPOLOGY

Symplectic Geometry; Symplectic structure; Symplectic topology

Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form. Symplectic geometry was founded by the Russian mathematician Vladimir Arnold and has its origins in the Hamiltonian formulation of classical mechanics where the phase space of certain classical systems takes on the structure of a symplectic manifold.

https://en.wikipedia.org/wiki/Symplectic_geometry

Transfer operator

PUSHFORWARD ON THE SPACE OF MEASURABLE FUNCTIONS

Ruelle operator; Perron-Frobenius operator; Perron-Frobenius Operator; Frobenius-Perron operator; Bernoulli operator; Ruelle-Frobenius-Perron operator; Frobenius–Perron operator; Perron–Frobenius operator

In mathematics, the transfer operator encodes information about an iterated map and is frequently used to study the behavior of dynamical systems, statistical mechanics, quantum chaos and fractals. In all usual cases, the largest eigenvalue is 1, and the corresponding eigenvector is the invariant measure of the system.

https://en.wikipedia.org/wiki/Transfer_operator

Wikipédia

Symplectic matrix

In mathematics, a symplectic matrix is a $2n\times 2n$ matrix $M$ with real entries that satisfies the condition

where $M^{\text{T}}$ denotes the transpose of $M$ and $\Omega$ is a fixed $2n\times 2n$ nonsingular, skew-symmetric matrix. This definition can be extended to $2n\times 2n$ matrices with entries in other fields, such as the complex numbers, finite fields, p-adic numbers, and function fields.

Typically $\Omega$ is chosen to be the block matrix

where

I_{n}

is the

n\times n

identity matrix. The matrix

\Omega

has determinant

+1

and its inverse is

\Omega ^{-1}=\Omega ^{\text{T}}=-\Omega

.

https://en.wikipedia.org/wiki/Symplectic matrix