Lectures related to Non-linear dynamics

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.

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.

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.

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.

Canonical Transformations: Symplectic Group and Properties

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

Bulky Hamiltonian isotopies

Explores the concept of bulky Hamiltonian isotopies of Lagrangian tori.

Canonical Transformations: Hamilton-Jacobi Equation

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

Analytical Mechanics: Lagrange Formalism

Covers the limitations of Lagrange formalism and the transition to Hamiltonian formalism for dynamic variables.

Molecular dynamics under constraints

Explores molecular dynamics simulations under holonomic constraints, focusing on numerical integration and algorithm formulation.

Linear Dynamics: Hamiltonians and Machine Elements

Explores Hamiltonians for machine elements, focusing on drift space, magnets, and linear maps.

Symplectic Rigidity: Forms of Symplectic Rigidity

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

Linear Beam Dynamics

Covers the Hamiltonian formalism, linear equations, Courant-Snyder parametrization, and chromatic effects in accelerator physics.

Hamiltonian Mechanics: Phase Space and Poisson Bracket

Explores phase space, the Poisson bracket, and Hamiltonian mechanics concepts.

Volume Growth of Positive Contactomorphisms

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

Canonical Transformations in Analytical Mechanics

Explores canonical transformations, conservation of quantities, and differential equations in analytical mechanics.

Canonical Equations: Solutions and Impulses

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

Canonical Transformations: Hamiltonian Equations

Explores canonical transformations, emphasizing Hamiltonian equations, constant quantities, and the importance of Lagrangian variables.