Dynamical Systems, Graphs, and Algorithms

Symbolic Image.- Periodic Trajectories.- Newton's Method.- Invariant Sets.- Chain Recurrent Set.- Attractors.- Filtration.- Structural Graph.- Entropy.- Projective Space and Lyapunov Exponents.- Morse Spectrum.- Hyperbolicity and Structural Stability.- Controllability.- Invariant Manifolds.- Ikeda Mapping Dynamics.- A Dynamical System of Mathematical Biology.

From the reviews:
"This book provides a taster for using symbolic analysis, graph theory, and set-oriented methods in a quest to understand the global structure of the dynamics in a continuous- or discrete-time system. In many ways, the techniques discussed here are complementary to more traditional ways of analysing a dynamical system and as such, this book can be viewed as a valuable entry into the theory and computational methods. … The book is intended for postgraduate researchers … ." (Hinke M. Osinga, Mathematical Reviews, Issue 2008 i)
"This monograph contains a summary of the author’s work on constructive methods for the study of discrete dynamical systems. … The structure of the book is very clear with 14 chapters devoted to different dynamical objects such as chain recurrent sets, structural stability or invariant manifolds, followed by two examples: the Ikeda mapping and a discrete food-chain model. … is certainly a valuable and very readable reference, in particular for the study of low-dimensional concrete systems with complicated dynamics." (Jörg Härterich, Zentralblatt MATH, Vol. 1130 (8), 2008)