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Lecture
Small Scale Stability: Gradient Systems
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Periodic Orbits of Hamiltonian Systems
Covers Morse theory, critical points, and Conley-Zehnder index in Hamiltonian systems.
Large Scale Stability Analysis
Covers large scale stability analysis and properties of dynamical systems solutions.
Small Scale Stability: Equilibrium Point
Covers small scale stability at equilibrium points in dynamical systems for engineers.
Lyapunov Stability in Dynamical Systems
Covers Lyapunov stability in dynamical systems, focusing on global asymptotic stability and practical implementation through semidefinite programming.
Mild Dissipative Surface Dynamics
Explores mild dissipative surface dynamics, including conservative behavior and ergodic functions.
Quantum Chaos and Scrambling
Explores the concept of scrambling in quantum chaotic systems, connecting classical chaos to quantum chaos and emphasizing sensitivity to initial conditions.
Compact Embedding: Theorem and Sobolev Inequalities
Covers the concept of compact embedding in Banach spaces and Sobolev inequalities.
Mathematical Modeling in Chemistry and Biology
Covers mathematical modeling in chemistry and biology, including chemical reactions, enzymatic kinetics, and population dynamics.
Lyapunov Stability and Chebyshev Inequalities
Explores Lyapunov stability and Chebyshev inequalities in system analysis and control design.
Learning and Adaptive Control for Robots: SEDS & LPV-DS
Explores learning and adaptive control for robots through SEDS and LPV-DS, emphasizing stability, non-linear dynamics, and optimization.
