Related papers: On Rational $P$-Adic Dyanamical Systems

We consider steady states for a class of mechanical systems with particle-disk interactions coupled to two, possibly unequal, heat baths. We show that any steady state that satisfies some natural assumptions is ergodic and absolutely…

This paper investigates the difference between the circular and elliptical cases in one-on-one pursuit and evasion problems. Using the simultaneous differential equation derived by Barton and Eliezer, we derive a dynamical system based on…

Relations between points in the phase space are central to the study of topological dynamical systems. Since many of these relations share common properties, it is natural to study them within a unified framework. To this end, we introduce…

We explore thick accretion disks around rotating attractors. We detail the configurations analysing the fluid angular momentum and finally providing a characterization of the disk morphology and different possible topologies. Investigating…

The method of nonlinear realizations and the technique previously developed in arXiv:1208.1403 are used to construct a dynamical system without higher derivative terms, which holds invariant under the l-conformal Newton-Hooke group. A…

Let f be an entire function whose set of singular values is bounded and suppose that f has a Siegel disk such that f restricts to a homeomorphism of the boundary. We show that the Siegel disk is bounded. Using a result of Herman, we deduce…

In this paper, we study Random Dynamical Systems (RDSs) of homeomorphisms on the circle without a finite orbit. We characterize the topological dynamics of the associated semigroup by identifying the existence of invariant sets which are…

We prove that a singular-hyperbolic attractor of a 3-dimensional flow is chaotic, in two strong different senses. Firstly, the flow is expansive: if two points remain close for all times, possibly with time reparametrization, then their…

We survey over some recent applications of motivic homotopy theory in the definition and the study of $p$-adic cohomology theories. In particular, we revisit the proof of the $p$-adic weight-monodromy conjecture for smooth projective…

Interest in the dynamical arrest leading to a fluid --> solid transition in thermal and athermal systems has led to questions about the nature of these transitions. These jamming transitions may be dependent on the influence of extended…

In this article, we study the forward dynamical behavior of nonautonomous lattice systems. We first construct a family of sets $\{\mathcal{A}_\varepsilon(\sigma)\}_{\sigma\in \Sigma}$ in arbitrary small neighborhood of a global attractor of…

In this paper the author presents the results of the preliminary investigation of fractional dynamical systems based on the results of numerical simulations of fractional maps. Fractional maps are equivalent to fractional differential…

We consider dynamical systems generated by partially hyperbolic surface endomorphisms of class C^r with one-dimensional strongly unstable subbundle. As the main result, we prove that such a dynamical system generically admits finitely many…

The dynamics of wavepackets in a relativistic Dirac oscillator (DO) is considered. A comparison to nonrelativistic spin-orbit pendulum effect is discussed. Particular relativistic effects, like Zitterbewegung in spin motion, are found in…

A study of rational maps of the real or complex projective plane of degree two or more, concentrating on those which map an elliptic curve onto itself, necessarily by an expanding map. We describe relatively simple examples with a rich…

In this paper, we study the dynamical system analysis for a recently proposed decaying dark energy model, namely, Q-SC-CDM. First we investigate the stationary points to find the stable attractor solution under the conditions discussed…

We first consider the Hamiltonian formulation of $n=3$ systems in general and show that all dynamical systems in ${\mathbb R}^3$ are bi-Hamiltonian. An algorithm is introduced to obtain Poisson structures of a given dynamical system. We…

We define arithmetical and dynamical degrees for dynamical systems with several rational maps on projective varieties, study their properties and relations, and prove the existence of a canonical height function associated with divisorial…

Given a Z_p-linear local system over a smooth rigid space, we show that it is crystalline (resp. semi-stable) with respect to any smooth (resp. semi-stable) integral model if and only if its restrictions at many classical points are…

We compare various concepts of attractor in the context of non-autonomous dynamical systems. Then, we prove an appropriate version of the Pliss reduction principle for non-autonomous differential systems with rapidly oscillating…