# Courses Catalogue

### Syllabus of the course: * Special Topics in Condensed Matter Physics - Non Linear Dynamics *

In this web page we provide the syllabus of the course Special Topics in Condensed Matter Physics - Non Linear Dynamics, offered by the Department of Physics.

The list of the courses offered during the current accademic year is available here.

The list of all courses offered by the Department of Physics is available here.

Code | Φ-842 |
---|---|

Type | B |

ECTS | 5 |

Hours | 4 |

Semester | Spring |

Instructor | I. Chitzanidi |

Program | Tuesday, 16:00-18:00, 2st floor semminar room Wednesday, 11:00-13:00, 2st floor semminar room |

Web page | https://eclass.physics.uoc.gr/courses/PH842/ |

Goal of the course | The course is addressed to postgraduate students and undergraduates with the appropriate background, Classical Mechanics (Φ-204) and Differential Equations I (Φ-211). It is an introductory course to the basic concepts of Dynamical Systems and Chaos, and their methods of analysis. |

Syllabus | 1. One-dimensional systems and elementary bifurcations 2. Two-dimensional systems; phase plane analysis, limit cycles, Poincaré-Bendixson theory 3. Nonlinear Oscillators, qualitative and approximate asymptotic techniques, Hopf bifurcations 4. Lorenz and Roessler equations, chaos, strange attractors and fractals 5. Iterated mappings, period-doubling, chaos 6. Hamiltonian systems; complete integrability and ergodicity 7. Area preserving mappings, KAM theory 8. Floquet theory 9. Applications of nonlinear dynamics |

Bibliography | "Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering", S. H. Strogatz, Westview Press, 2000 "Introduction to nonlinear science", G. Nicolis, Cambridge University Press, Cambridge, 1995 "Nonlinear Ordinary Differential Equations", ''Nonlinear Systems'',P. G. Drazin, Cambridge University Press, Cambridge, 1992 ''Nonlinear Oscillations, Dynamical Systems'' Guckenheimer and Holmes, Springer, 1983. |

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