Almost oscillatory three-dimensional dynamical system

Almost oscillatory three-dimensional dynamical system

* Correspondence: [email protected] Missouri University of Science and Technology, 310 Rolla Building, Missouri 65409-0020, USA Full list of author information is available at the end of the article Abstract In this article, we investigate oscillation and asymptotic properties for 3D systems of dynamic equations. We show the role of nonlinearities and we apply our results to the adjoint dynamic sys...

Pointwise almost periodicity in a generalized shift dynamical system

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Almost Block Independence for the Three Dot Z Dynamical System

We show that the measure preserving action of Z2 dual to the action defined by the commuting automorphisms ×x and ×y on the discrete group Z[x±1, y±1]/〈1 +x+ y〉Z[x±1, y±1] is measurably isomorphic to a Z2 Bernoulli shift. This was conjectured in recent work by Lind, Schmidt and the author, where it was shown that this action has completely positive entropy. An example is given of Z2 actions whi...

The Three-Dimensional Gauss Algorithm Is Strongly Convergent Almost Everywhere

Finite-dimensional dynamical system modeling thermal instabilities

We describe a three-dimensional dynamical system, which is obtained as a pseudo-spectral approximation to a free boundary problem modeling solid combustion and rapid solidification, and is capable of generating its major dynamical patterns. These patterns include a Hopf bifurcation followed by a sequence of secondary period doubling and a transition to chaos, reverse sequences, and sequences fo...