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Non-linear dynamics
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Related lectures (32)
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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.
Symplectic Geometry
Covers the background on symplectic geometry, focusing on symplectic manifolds and canonical structures.
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.
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.
Weil Representation and Heis Operators
Covers the Weil representation, Heis operators, Stone-Neumann theorem, unitary operators, Lie algebra structure, and symplectic form.
Linear Beam Dynamics
Explores particle accelerator dynamics, transfer maps, Hamiltonian equations, and phase space conservation.
Periodic Orbits of Hamiltonian Systems
Explores periodic orbits in Hamiltonian systems and their stability under various conditions.
Canonical Transformations 2
Explores canonical transformations, symplectic matrices, and the concept of identity in matrix space.
Periodic Orbits of Hamiltonian Systems
Covers the theory of periodic orbits of Hamiltonian systems and the Conley-Zehnder index.
Canonical Equations and Integrable Systems
Explores canonical equations, integrable systems, trajectories, and the symplectic matrix in understanding system dynamics.
