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Lecture
Small Scale Stability: Gradient Systems
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Small Scale Stability: Gradient Systems
Explores small scale stability in gradient systems, analyzing trajectories and attractors in phase space.
Dimension theory of rings
Covers the dimension theory of rings, including additivity of dimension and height, Krull's Hauptidealsatz, and the height of general complete intersections.
Special Types of Systems: Limit Cycles
Covers special types of systems, focusing on gradient systems and limit cycles, discussing equilibrium points, stability, and chaotic behavior.
Physics 1: Harmonic Oscillator and Spherical Coordinates
Explores harmonic oscillators, pendulum movement, and spherical coordinates in physics.
Principal Ideal Domains: Structure and Homomorphisms
Covers the concepts of ideals, principal ideal domains, and ring homomorphisms.
Mild Dissipative Surface Dynamics
Explores mild dissipative surface dynamics, including conservative behavior and ergodic functions.
Shell Components in Meromorphic Parameter Spaces
Explores shell components in transcendental parameter planes and attracting cycles.
Polynomials on a Field: Basics and Operations
Introduces the basics of polynomials on a field, focusing on definitions, operations, and properties.
Dimension Theory of Rings
Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.
Nonlinear Dynamics and Chaos
Covers bifurcations, long-term dynamics, logistic map, universality, and correspondence between different maps.
