We present the logarithm laws for the partial sum of the itinerary function over non-periodic BCZ orbits, utilizing the even and odd Diophantine exponent defined by Athreya-Margulis. We also give a detailed description of the BCZ map and its excursions.
In this article we continue to study the concept of entropy introduced in [4], [15]-[17]. We calculate entropy for a wider class of finite-dimensional operators in comparison with [15]. We also approximate the entropy of a unitary operator on $l^2(\mathbb{N}_0)$ by the entropy of finite-dimensional operators. Finally we calculate the entropy of several operators on $l^2(\mathbb{N}_0)$.
Let (X,Z) be a dynamical system on a compact metric X and let X be the countable union of closed invariant subsets X_i, i in N. We prove that mdim X =sup {mdim X_i : i in N}.
We show that the Jouanolou foliation of degree 2 on the complex projective plane is structurally stable. Moreover, its Fatou set is a fibration on the Klein quartic with the structure of a smooth fiber bundle in disks. In particular, there is no dense leaf.
We prove that the boundary of every parabolic component in the cubic polynomial slice $Per_1(1)$ is a Jordan curve by adapting the technique of para-puzzles presented in \cite{Roesch1}. We also give a global description of the connected locus $\mathcal{C}_1$: it is the union of two main parabolic components and the limbs attached on their boundaries.
Given a quasiperiodic cocycle in sl(2, R) sufficiently close to a constant, we prove that it is almost-reducible in ultradifferentiable class under an adapted arithmetic condition on the frequency vector. We also give a corollary on the H{ö}lder regularity of the Lyapunov exponent.
Agradecemos la participación de los siguientes árbitros: Ivannia Sofía Soto Monge, Universidad Creativa, Costa Rica María Elisa Velázquez Gutiérrez, Instituto Nacional de Antropología e Historia, México Olivia Fragoso Susunaga, Universidad Autónoma Metropolitana, México Cintia Daiana Garrido, Universidad del Cine (FUC), Argentina Jorge León Casero, Universidad de Zaragoza, España Mariel Andrea Manrique Rivera, Escuela Nacional de Antropología e Historia, México César Enrique Vega Dávila, Universidad Iberoamericana, México Julieta Pérez Monroy, Universicidad Nacional Autónoma de México, México Guillermina Valent, Universidad Nacional de La Plata, Argentina Paola Sabrina Belén, Universidad Nacional de La Plata, Argentina
The abstract hyperbolic sets are introduced. Continuous and differentiable mappings as well as rate of convergence and transversal manifolds are not under discussion, and the symbolic dynamics paradigm is realized in a new way. Our suggestions are for more neat comprehension of chaos in the domain. The novelties can serve for revisited models as well as motivate new ones.
We prove existence and compute the limiting distribution of the image of rank-$\left(d-1\right)$ primitive subgroups of $\mathbb{Z}^{d}$ of large covolume in the space $X_{d-1,d}$ of homothety classes of rank-$\left(d-1\right)$ discrete subgroups of $\mathbb{R}^{d}$. This extends a theorem of Aka, Einsiedler and Shapira.
This paper develops the singular perturbation theory for a particular discrete-time nonlinear system which models the saturating inductor buck converter using cycle-by-cycle digital control.
Agradecemos la participación de los siguientes árbitros: Edgar Cortez Guamba, Universidad Central, Ecuador Antonio Guzmán Quintana, Universidad Viña del Mar, Chile Isabel Galindo Aguilar, Escuela Nacional de Antropología e Historia, México Marcelo Zevallos Rimondi, Escuela Nacional Superior Autónoma de Bellas Artes, Perú Mark Betts Alvear, Universidad del Norte, Colombia Carolina Marrugo Orozco, Independiente, Colombia Carlos Castrillón Castro, Universidad Iberoamericana, México
The existence of an aperiodic orbit for an outer billiard outside a regular octagon is proved. Additionally, almost all orbits of such an outer billiard are proved to be periodic. All possible periods are explicitly listed.
Under the assumption of the gluing orbit property, equivalent conditions to having zero topological entropy are investigated. In particular, we show that a dynamical system has the gluing orbit property and zero topological entropy if and only if it is minimal and equicontinuous.
We apply the general normal form theorems in Kolmogorov spaces to three classical cases: deformations of hypersurface singularities, normal forms of vector fields and invariant tori in Hamiltonian systems.
We construct a diffeomorphism $f$ on 2-torus with a dominated splitting $E \oplus F$ such that there exists an open neighborhood $\mathcal{U} \ni f$ satisfying that for any $g \in \mathcal{U}$, neither $E_g$ nor $F_g$ is integrable.
Via (C,F)-construction we produce a 2-fold simple mixing transformation which has uncountably many non-trivial proper factors and all of them are prime.