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Books. Invitation to Dynamical Systems (Prentice Hall, 1996, reprinted by Dover Publications, 2012).; Fractional Graph Theory (With Daniel Ullman, Wiley, 1997 ...
The Poincaré map for the dynamical system associated with the Kronecker foliation on a torus with angle θ> is the irrational rotation by θ. C*-algebras associated with irrational rotations, known as irrational rotation algebras, have been extensively studied.
Dynamical systems theory and chaos theory deal with the long-term qualitative behavior of dynamical systems.Here, the focus is not on finding precise solutions to the equations defining the dynamical system (which is often hopeless), but rather to answer questions like "Will the system settle down to a steady state in the long term, and if so, what are the possible steady states?", or "Does ...
Hendrik Wolter "Henk" Broer (born 18 February 1950, Diever) is a Dutch mathematician known for contributions to the theory of nonlinear dynamical systems. He was professor at the University of Groningen between 1981 and 2015.
Conley's decomposition is characterized by a function known as complete Lyapunov function. Unlike traditional Lyapunov functions that are used to assert the stability of an equilibrium point (or a fixed point) and can be defined only on the basin of attraction of the corresponding attractor, complete Lyapunov functions must be defined on the whole phase-portrait.
The ergodic theory of dynamical systems has recently been used to prove combinatorial theorems about number theory which has given rise to the field of arithmetic combinatorics. Also dynamical systems theory is heavily involved in the relatively recent field of combinatorics on words. Also combinatorial aspects of dynamical systems are studied.
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Dynamical systems deals with the study of the solutions to the equations of motion of systems that are primarily mechanical in nature; although this includes both planetary orbits as well as the behaviour of electronic circuits and the solutions to partial differential equations that arise in biology.