Structure and Bifurcations of Dynamical Systems

The contents of this volume consist of 15 lectures on mathematics and its applications which include the following topics: dynamics of neural network, phase transition of cellular automata, homoclinic bifurcations, ergodic theories of low dimensional dynamical systems, Anosov endomorphisms and Anosov flows, axiom A systems, complex dynamical systems, multi-dimensional holomorphic dynamical systems and holomorphic vector fields.

Sample Chapter(s)
Nonlinear Associative Dynamics and Pattern Representations in Chaotic Neural Networks (2,009 KB)

• Nonlinear Associative Dynamics and Pattern Representations in Chaotic Neural Networks (T Ikeguchi et al.)
• Neural Networks, Approximation Theory, and Dynamical Systems (K Funahashi & Y Nakamura)
• Switched Dynamical Systems — Dynamics of a Class of Circuits with Switch (H Kawakami & R Lozi)
• Evolutionary Dynamics of Complex Systems: Self-Organization toward Criticality at the Border between Order and Chaos (Y Gunji & K Ito)
• N-Homoclinic Bifurcations of Piecewise Linear Vector Fields (K Iori et al.)
• A Classification of Cusp-Type Maps (T Inoue)
• Infinitesimal Stability of Anosov Endomorphisms (H Ikeda)
• On Jakobson's Theorem (M Tsujii)
• Geometric Approach to Ratner's Rigidity Theorem and its Extension (R Abe)
• Transverse Invariant 1-Forms for Anosov Flows on 3-Manifolds (N Watanabe)
• Poisson's Law for Axiom A System (M Hirata)
• On Quasiconformal Equivalence on the Boundary of the Tricorn (S Nakane)
• Böttcher's Theorem and Super-Stable Manifolds for Multidimensional Complex Dynamical Systems (S Ushiki)
• Remarks on Holomorphic Vector Fields in C² and Invariants of the Graph Links (N Oka)
• The Mandelbrot Set and Kneading Sequences (A Kameyama)