Symplectic Geometry

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Related lectures (30)

Page 1 of 3

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

Non-linear dynamics

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

Lie Algebra: Vector Space and Multiplication Law

Covers Lie Algebra, focusing on vector space and multiplication law.

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.

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

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.

Hilpot Liegr: Understanding Nilpotent Lie Groups

Explores nilpotent Lie groups, their orbits, and adjoint actions, illustrating simplicity and form.

Nilpotent Lie Groups

Covers the properties of nilpotent Lie groups and the construction of non-degenerate alternating 2-forms.

Complete Reducibility of Complex Representations

Covers the complete reducibility of complex representations and the relation between Lie algebras and Lie groups.

Integral Curves and Exponential Map

Explores integral curves on manifolds and the significance of the exponential map in Lie groups.