Corso di Sistemi Dinamici, anno accademico 2025-2026. 8 CFU.
Diario delle lezioni
  1. Lecture of 01/10/2025: Esistenza e unicità delle soluzioni delle ODE.
  2. Lecture of 02/10/2025: Floquet theroy. Analytic function calculus.
  3. Lecture of 07/10/2025: Analytic function calculus and perturabtion theory.
  4. Lecture of 09/10/2025: Perturabtion theory and naive qualitative study of ODE.
  5. Lecture of 10/10/2025: Deleted for strike in the transportation system. Missed hours will be made up in the two upcoming lessons.
  6. Lecture of 14/10/2025: Flow box theorem.
  7. Lecture of 16/10/2025: Grobman-Hartman Theorem.
  8. Lecture of 17/10/2025: Hadamard-Perron Theorem.
  9. Lecture of 21/10/2025: Topology and the concept of genericity. Generic vector fields.
  10. Lecture of 23/10/2025: Generic families of vector fields and saddle-node biforcations.
  11. Lecture of 28/10/2025: Holf bifurcations.
  12. Lecture of 30/10/2025: Limit sets and Poincarè-Bendixon Theorem.
  13. Lecture of 31/10/2025: Constant vector fields on the Torus. Siegel global section.
  14. Lecture of 04/11/2025: Homeomorphisms of the circle and rotation number.
  15. Lecture of 06/11/2025: Diffeomorphisms of the circle.
  16. Lecture of 07/11/2025: KAM for circle maps.
  17. Lecture of 11/11/2025: KAM for circle maps.
  18. Lecture of 13/11/2025: Perturbed Pendulum.
  19. Lecture of 18/11/2025: Measurable dynamical systems. Ergodicity, Birkhoff, Von Neumann
  20. Lecture of 20/11/2025: Recurrence. Mixing. Examples. Logistic map.
  21. Lecture of 21/11/2025: Transfer operators and invariant measures.
  22. Lecture of 25/11/2025: Fixed point Theorems.
  23. Lecture of 27/11/2025: A bit of Functional analysys (Hilbert metric and Birkhoff theorem). Unique invariant measure absolutely continuous with respect to Lebesgue for expanding maps.
  24. Lecture of 02/12/2025: More functional analysis (Hennion Theorem).
  25. Lecture of 04/12/2025: Piecewise expanding maps.
  26. Lecture of 05/12/2025: Stability of the transfer operator spectra.
  27. Lecture of 09/12/2025: Teoremi limite (CLT).
  28. Lecture of 11/12/2025: Teoremi limite (Large deviations).
  29. Lecture of 12/12/2025: Transfer operator for Anosov maps (Functional analysis).
  30. Lecture of 16/12/2025: Transfer operator for Anosov maps (Functional analysis).
  31. Lecture of 18/12/2025: Anosov flows. Partially hyperbolic systems.
  32. Lecture of 19/12/2025: Non-unformly hyperbolic systems.