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Concept

Symplectic manifold

Related lectures (32)

Symplectic Rigidity: Forms of Symplectic Rigidity

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

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.

Optimization on Manifolds: Context and Applications MOOC: Introduction to optimization on smooth manifolds: first order methods

Introduces optimization on manifolds, covering classical and modern techniques in the field.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Volume Growth of Positive Contactomorphisms

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

Canonical Transformations 2

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

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.

Periodic Orbits of Hamiltonian Systems

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

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Periodic Orbits of Hamiltonian Systems

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

Bulky Hamiltonian isotopies

Explores the concept of bulky Hamiltonian isotopies of Lagrangian tori.

Forcing of Topological Entropy

Delves into topological entropy in compact manifolds and Reeb flows, emphasizing the forcing of entropy via cylindrical contact homology.

Smooth Manifolds: Setup MOOC: Introduction to optimization on smooth manifolds: first order methods

Introduces smooth manifolds, emphasizing the importance of submanifolds of linear spaces.

Gateways to the Moon and Local Floer Homology

Explores the problem of a falling stone hitting the moon, focusing on gateways to the moon and local Floer homology.

Riemannian metrics and gradients: Computing gradients from extensions MOOC: Introduction to optimization on smooth manifolds: first order methods

Explores computing gradients on Riemannian manifolds through extensions and retractions, emphasizing orthogonal projectors and smooth extensions.

What is a smooth manifold? - Through defining functions MOOC: Introduction to optimization on smooth manifolds: first order methods

Explores smooth manifolds through defining functions and submanifolds, highlighting the importance of smoothness.

Tangent Spaces and Submersions

Covers tangent spaces and submersions in differential geometry, emphasizing vector spaces and differentiable structures.

From embedded to general manifolds: upgrading our foundations

Explores the transition from embedded to general manifolds, upgrading foundational concepts and discussing mathematical reasons for both approaches.

Infinitesimal Deformations: One-Dimensional Maps

Explores infinitesimal deformations of one-dimensional maps, discussing common characteristics, methods, and recent results in expanding and piecewise expanding maps.