Instructor: Dr. Imre Péter TOTH
Text: C. Robinson: Dynamical Systems: Stability, Symbolic Dynamics,
and Chaos. second edition; CRC Press, 1999
Additional information about the book may be found at here.
The book will not be sold at the BSM bookstore. You can buy it Amazon.com
or borrow from one of these libraries in Budapest:
Library of the
Rényi Institute
Library of SzTAKI
(Computer and Automation Research Institue)
Library of the Mathematical
Institute of BUTE (Budapest University of Technology and Economics)
Central Library of BUTE
(Budapest University of Technology and Economics)
The first two chapters of the book will be distributed free of
charge
Prerequisite: - calculus: limits, differentiation,
continuity, open/closed sets, metric space,
- linear algebra: Euclidean space, matrix of a linear
mapping, eigenvalues, eigenvectors of a linear mapping; canonical form
Course description:
- differential equations and iterated maps as dynamical systems (Chapter I)
- one-dimensional maps (Chapter II)
- the quadratic family (Section
2.2)
- symbolic dynamics (Sections
2.4, 2.5)
- limit sets and recurrence
(Section 2.3)
- conjugacy (Sections 2.6,
2.7)
- structural stability (Sections
2.6, 2.7)
- period doubling bifurcation
(Sections 3.4, 7.3)
- higher dimensional systems
- phase portraits of linear
diifferential equations (Chapter IV)
- hyperbolicity, Lyapunov
exponents (Sections 3.6, 4.6)
- fixed points for nonlinear
differential equations (Section 5.5)
- Hartman-Grobman Theorem (Section 5.6)
- suspension of a map; Poincar\'e
map for differential equations (Section 5.8)
- bifurcation of periodic
points (Chapter VII)
- transitivity theorems
(Section 8.2)
- Smale Horseshoe ((Section
8.4)
- CAT map; Markov partition
for hyperbolic toral automorphisms (Section 8.5)
- Lorenz attractor (Section
8.11)
- Hamiltonian systems (Sections
6.1, 6.3)
- KAM Theorem (Section 6.5)