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Leonov, G. A., Reitmann, V., Timmermann, W.; (Eds.)
Nonlinear Dynamics and Quantum Dynamical Systems.
(Contributions to the International Seminar ISAM-90 held in Gaussig,
March 19--23, 1990).
Mathematical Research 59. Akademie-Verlag, Berlin 1990.
168 p.
Book review
These Contributions to the International Seminar ISAM-90 were published as Vol. 59
of "Mathematical Research". Aulbach and Hilger in "Linear Dynamic Processes with
Inhomogeneous Time Scale" present a calculus which provides a smooth transition
from the discrete- to the continuous-case. Belykh in "Bifurcations and Attractors
of phase Systems" considers esp. the Lorenz equation in the system
rotator-oscillator. Hudetz in "Algebraic Topological Entropy" is concerned both
with topological and algebraic variational principle. Kästner and Zylka in
"An Application of Majorization in the Theory of Dynamical Systems"
are concerned with accessibility problem.
Koksch's paper both title and summary is "On Application of Ljapunov Functions
and Comparison Systems to Analysis of Stability for Nonlinear Ordinary Differential
Equations". Leonov in "Orbital Stability and Problems of Nonlocal Dynamics" is
concerned with strong orbital instability as a characteristic of strangeness of
attractors with application to Lorenz equation. Moebius in "About the Structure
of Conserved Quantities of Special Many-Body Systems", the special means
one-dimensional particles. Narnhofer in "K-Automorphisms in
"Quantum Theory"
is concerned with mixing properties. Quasthoff and Schüler in "Cellular
Automata and Symbolic Dynamics" are considering one sided, one dimensional such
automata. Reich's "On a Geometric Characterization of Differential-Algebraic
Equations" was inspired by nonlinear electrical networks. Reitmann in "
Asymptotic
Behaviour of Trajectories of Dynamical Systems on the Cylinder" considers such
systems as models of phase synchronization, coupled Josephson junctions and
other systems with angular coordinates and introduces the feedback into such
systems. Schneider and Wegner in "On the Limits of Periods of Closed Trajectories
Contracting to an Equilibrium Point" contribute to the Hopf Bifurcation. Smirnova
in "Stability of Singular Distributed Dynamical Systems with Angular Coordinates"
was inspired by phase-locked loops and synchronous electric motors described by
Volterra equations. Timmermann in "Quantum Dynamics and Algebras" of Unbounded
Operators concentrates on the dissipative operators. Finally, Wunsch in his
"Mechanics from a System Theoretic Point of View" is concerned with
Markov processes.
Antonin Vanécek,
Nove knigy - Kybernetika 27/6/91
