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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 ...
Irrational rotations form a fundamental example in the theory of dynamical systems.According to the Denjoy theorem, every orientation-preserving C 2-diffeomorphism of the circle with an irrational rotation number θ is topologically conjugate to T θ.
He has worked on applications of category theory, in particular ologs and operadic compositionality of dynamical systems. He authored and coauthored the introductory texts on category theory and its applications, Category Theory for the Sciences and An Invitation to Applied Category Theory.
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 ...
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.
LaSalle's invariance principle (also known as the invariance principle, [1] Barbashin-Krasovskii-LaSalle principle, [2] or Krasovskii-LaSalle principle) is a criterion for the asymptotic stability of an autonomous (possibly nonlinear) dynamical system.
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Projected dynamical systems is a mathematical theory investigating the behaviour of dynamical systems where solutions are restricted to a constraint set. The discipline shares connections to and applications with both the static world of optimization and equilibrium problems and the dynamical world of ordinary differential equations.