- Docente: Marco Lenci
- Crediti formativi: 6
- SSD: MAT/07
- Lingua di insegnamento: Inglese
- Moduli: Natale Alberto Carrassi (Modulo 1) Marco Lenci (Modulo 2)
- Modalità didattica: Convenzionale - Lezioni in presenza (Modulo 1) Convenzionale - Lezioni in presenza (Modulo 2)
- Campus: Bologna
- Corso: Laurea Magistrale in Science of Climate (cod. 5895)
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Orario delle lezioni (Modulo 1)
dal 16/09/2024 al 17/12/2024
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Orario delle lezioni (Modulo 2)
dal 30/09/2024 al 19/12/2024
Conoscenze e abilità da conseguire
At the end of the course, the student possesses the basic knowledge on complex physical, biological and social systems and on the means of analysis, predictability and control. In particular, the student is able to: - solve problems of deterministic chaos and predictability; - solve problems of emerging self-organization; - develop a project with object-oriented architecture and advanced graphics, using agent models and network theory.
Contenuti
Slightly tentative syllabus:
Basic definitions of dynamical systems: generalities and standard examples. Stability: general concepts. Assessing stability via linearization or Lyapunov functions. Periodic solutions. Poincaré-Bendixon theorem. Stable and unstable manifolds. The statistical point of view for deterministic dynamical systems. Elementary ergodic theory. Hyperbolicity as the main ingredient for chaos. Attractors and basins of attraction. Structural stability. Bifurcations. In time permits: Elements of entropy in dynamical systems. Concepts of predictability. Intermittency.
Testi/Bibliografia
Lenci's part:
The course will draw from no specific text. There are some reference texts for various topics and for further readings:
- P. Walters, An introduction to ergodic theory, Springer
- B. Hasselblatt & A. Katok, A first course in dynamics, Cambridge U. Press
- V. I. Arnold & A. Avez, Ergodic problems of classical mechanics, Addison-Wesley
Metodi didattici
Classroom lectures
Modalità di verifica e valutazione dell'apprendimento
The final assessment will be in the form of an oral exam (30-60 mins) where the student will be asked a number of questions aimed at evaluating the student's degree of understanding of the concepts, methods, and problems explained in the course. The student will also be asked to solve at least a (simple) exercise.
Strumenti a supporto della didattica
Notes handed by the instructor.
Orario di ricevimento
Consulta il sito web di Marco Lenci
Consulta il sito web di Natale Alberto Carrassi