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Concept

Symplectic vector space

Related lectures (24)

Non-linear dynamics

Explores practical applications in nonlinear dynamics, emphasizing symplectic integration methods and thin lens approximations for accurate computations in accelerator physics.

Essential Coexistence Phenomenon in Hamiltonian Dynamics

By Yakov Pesin delves into the essential coexistence phenomenon in Hamiltonian dynamics, exploring types I and II and providing examples and proofs.

Symplectic Rigidity: Forms of Symplectic Rigidity

Explores symplectic rigidity, including rigidity, flexibility, and dynamical rigidity, with a focus on symplectic manifolds and Lagrangian submanifolds.

Canonical Transformations 2

Explores canonical transformations, symplectic matrices, and the concept of identity in matrix space.

Volume Growth of Positive Contactomorphisms

Covers the growth of positive contactomorphisms in Legendrian spheres and symplectic forms.

Non-linear dynamics: phenomenology, tools and methods

Explores Hamiltonian and Lagrangian formulations, canonical variables, Lie operators, and their applications in beam dynamics and nonlinear systems.

Canonical Transformations: Properties and Applications

Explores canonical transformations, their properties, and applications in Hamiltonian mechanics, emphasizing their role in simplifying the analysis of complex systems.

Canonical Transformations: Symplectic Group and Properties

Explores canonical transformations, symplectic groups, real matrices, preserved quantities, and volumes in phase space.

Canonical Transformations: Hamilton-Jacobi Equation

Explores canonical transformations, the Hamilton-Jacobi equation, symplectic groups, and differential equations in physics.

Periodic Orbits of Hamiltonian Systems

Explores periodic orbits in Hamiltonian systems and their stability under various conditions.

Periodic Orbits of Hamiltonian Systems

Covers the theory of periodic orbits of Hamiltonian systems and the Conley-Zehnder index.

Canonical Equations: Solutions and Impulses

Explores canonical equations for isolated systems, finding solutions and analyzing impulses.

Canonical Equations and Integrable Systems

Explores canonical equations, integrable systems, trajectories, and the symplectic matrix in understanding system dynamics.

Linear Beam Dynamics

Explores particle accelerator dynamics, transfer maps, Hamiltonian equations, and phase space conservation.

Curves with Poritsky Property and Liouville Nets

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Dynamics of Steady Euler Flows: New Results

Explores the dynamics of steady Euler flows on Riemannian manifolds, covering ideal fluids, Euler equations, Eulerisable flows, and obstructions to exhibiting plugs.

Symplectic Geometry Log in to Mediaspace to watch this video

Covers the background on symplectic geometry, focusing on symplectic manifolds and canonical structures.

The Weil Representation: Part 2 Log in to Mediaspace to watch this video

Covers the Weil representation, Heisenberg group actions, and symplectic group concepts.

Harmonic Oscillator: Numerical Stability Analysis Log in to Mediaspace to watch this video

Explores the numerical stability of the harmonic oscillator and the importance of improving digital diagrams.

Weil Representation and Heis Operators Log in to Mediaspace to watch this video

Covers the Weil representation, Heis operators, Stone-Neumann theorem, unitary operators, Lie algebra structure, and symplectic form.