Kakutani fixed-point theorem

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Explores the Kuramoto model for synchronization in phase oscillators and discusses stability criteria and critical coupling values.

Covers the movement of a grinding wheel on a non-slip bearing and the physics of a rotating thin disc.

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Explores critical behavior in general relativity, including scaling factor and coupling constant flow.

Explores the analysis of a ball's trajectory in contact with a beam, focusing on forces, angles, and motion equations.

Covers dynamic systems, trajectories, growth models, stability of fixed points, and linearization of models.

Explores the existence and uniqueness of solutions for differential equations through local Lipschitz continuity and the Cauchy-Lipschitz theorem.

Covers the application of functions defined by recurrence to sequences and the theorem of the fixed point.

Explores the Renormalization Group in field theory, discussing scaling functions, critical exponents, and Gaussian fixed points.

Covers the convergence of fixed point methods for nonlinear equations, including global and local convergence theorems and the order of convergence.