Related papers: Rotation Numbers for Random Dynamical Systems on t…
The goals of this paper are to obtain theoretical models of what happens when a computer calculates the rotation set of a homeomorphism, and to find a good algorithm to perform simulations of this rotation set. To do that we introduce the…
Analyzing the dynamics of open quantum systems has a long history in mathematics and physics. Depending on the system at hand, basic physical phenomena that one would like to explain are, for example, convergence to equilibrium, the…
Open dynamical systems are mathematical models of machines that take input, change their internal state, and produce output. For example, one may model anything from neurons to robots in this way. Several open dynamical systems can be…
We show that dimensional theoretical properties of dynamical systems can considerably change because of number theoretical peculiarities of some parameter values
In this work, Bernoulli's Law of Large Numbers, also known as the Golden theorem, has been extended to study the relations between empirical probability and empirical randomness of an otherwise random experiment. Using the example of a coin…
This paper shows the existence of independent random matching of a large (continuum) population in both static and dynamic systems, which has been popular in the economics and genetics literatures. We construct a joint agent-probability…
Generalizations of linear numeration systems in which the set of natural numbers is recognizable by finite automata are obtained by describing an arbitrary infinite regular language following the lexicographic ordering. For these systems of…
Symmetries are ubiquitous in a wide range of nonlinear systems. Particularly in systems whose dynamics are determined by a Lagrangian or Hamiltonian function. For hybrid systems which possess a continuous-time dynamics determined by a…
Motion control of underactuated systems through the inverse dynamics contains configuration singularities. These limitations in configuration space mainly stem from the inertial coupling that passive joints/bodies create. In this study, we…
Atypical, rare trajectories of dynamical systems are important: they are often the paths for chemical reactions, the haven of (relative) stability of planetary systems, the rogue waves that are detected in oil platforms, the structures that…
An important problem in the theory of finite dynamical systems is to link the structure of a system with its dynamics. This paper contains such a link for a family of nonlinear systems over an arbitrary finite field. For systems that can be…
We show that the dynamical degree of an (i.i.d) random sequence of dominant, rational self-maps on projective space is almost surely constant. We then apply this result to height growth and height counting problems in random orbits.
In this paper, we consider sufficient conditions for an invariant double circle to occur in a one parameter discrete dynamical systems on a cylinder.
We investigate the quantum recurrence phenomena in periodically driven systems. We calculate the classical period and the quantum recurrence time and develop their interdependence. We further predict the behavior of the recurrence phenomena…
The dynamical properties, especially the symmetric orbits, of the 2-parameter family of circle maps called off-center reflection is studied.
The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not…
The orientation of a rigid object can be described by a rotation that transforms it into a standard position. For a symmetrical object the rotation is known only up to multiplication by an element of the symmetry group. Such ambiguous…
Periodic orbits and cycles, respectively, play a significant role in discrete- and continuous-time dynamical systems (i.e. maps and flows). To succinctly describe their shifts when the system is applied perturbation, the notions of…
We continue previous work to count non-equivalent dynamical systems over finite fields generated by polynomials or rational functions.
In this paper, we will study the statistical behaviors of orbits. Firstly, we will show that for a dynamical systems have the shadowing property or almost specification property, the set of nonrecurrent points has full topological entropy.…