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Related papers: Dynamical properties of the negative beta transfor…

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We consider positional numeration system with negative base $-\beta$, as introduced by Ito and Sadahiro. In particular, we focus on arithmetical properties of such systems when $\beta$ is a quadratic Pisot number. We study a class of roots…

Number Theory · Mathematics 2010-11-08 Z. Masáková , T. Vávra

Let the map $f:[-1,1]\to[-1,1]$ have a.c.i.m. $\rho$ (absolutely continuous $f$-invariant measure with respect to Lebesgue). Let $\delta\rho$ be the change of $\rho$ corresponding to a perturbation $X=\delta f\circ f^{-1}$ of $f$. Formally…

Dynamical Systems · Mathematics 2009-11-10 David Ruelle

We study a one-parameter family of interval maps $\{T_\alpha\}_{\alpha\in[1,\beta]}$, with $\beta$ the golden mean, defined on $[-1,1]$ by $T_\alpha(x)=\beta^{1+|t|}x-t\beta\alpha$ where $t\in\{-1,0,1\}$. For each $T_\alpha,\ \alpha>1$, we…

Dynamical Systems · Mathematics 2023-01-23 Karma Dajani , Slade Sanderson

Given a totally finite ordered alphabet $ A $, endowing the set of words over $ A $ with the alternating lexicographic order, we define a new class of Lyndon words. We study the fundamental properties of the associated symbolic dynamical…

Dynamical Systems · Mathematics 2017-07-31 Florent Nguema Ndong

In this study, we have reported key nuclear properties of weak $\beta$-decay processes on Yttrium isotopes for the mass number range $A = 101 - 108$. This mass region is important in astrophysical $r$-process abundances. Our study might be…

Nuclear Theory · Physics 2025-03-24 Fakeha Farooq , Jameel-Un Nabi , Ramoona Shehzadi

The in-medium properties of $\eta$ mesons are studied in hot and dense isospin asymmetric strange magnetized matter using the chiral SU(3) hadronic mean-field model. The scalar and vector density of baryons are expressed in terms of thermal…

High Energy Physics - Phenomenology · Physics 2022-11-22 Shivanshi Tiwari , Rajesh Kumar , Manisha Kumari , Arvind Kumar

A generalization of the regular continued fractions was given by Burger et al. in 2008 [3]. In this paper we give metric properties of this expansion. For the transformation which generates this expansion, its invariant measure and…

Number Theory · Mathematics 2015-10-08 Dan Lascu

In some former works of Azzam and Tolsa it was shown that $n$-rectifiability can be characterized in terms of a square function involving the David-Semmes $\beta_2$ coefficients. In the present paper we construct some counterexamples which…

Classical Analysis and ODEs · Mathematics 2018-01-22 Xavier Tolsa

In this paper we study a class of \emph{self-consistent dynamical systems}, self-consistent in the sense that the discrete time dynamics is different in each step depending on current statistics. The general framework admits popular…

Dynamical Systems · Mathematics 2022-09-22 Fanni M. Sélley

We study real numbers $\beta$ with the curious property that the $\beta$-expansion of all sufficiently small positive rational numbers is purely periodic. It is known that such real numbers have to be Pisot numbers which are units of the…

Number Theory · Mathematics 2014-02-26 Boris Adamczewski , Christiane Frougny , Anne Siegel , Wolfgang Steiner

We derive a master equation for the reduced density matrix of a uniformly accelerating quantum detector in arbitrary dimensions, generically coupled to a field initially in its vacuum state, and analyze its late time regime. We find that…

General Relativity and Quantum Cosmology · Physics 2021-09-06 Julio Arrechea , Carlos Barceló , Luis J. Garay , Gerardo García-Moreno

$\beta$-decay properties of nuclei are investigated within the relativistic nuclear energy density functional framework by varying the temperature and density, conditions relevant to the final stages of stellar evolution. Both thermal and…

Nuclear Theory · Physics 2021-09-06 A. Ravlic , E. Yuksel , Y. F. Niu , N. Paar

Every symbolic system supports a Borel measure that is invariant under the shift, but it is not known if every such systems supports a measure that is invariant under all of its automorphisms; known as a characteristic measure. We give…

Dynamical Systems · Mathematics 2023-07-14 Van Cyr , Bryna Kra , Samuel Petite

We study the selfsimilarity and the Gibbs properties of several measures defined on the product space $\Omega\_r:=\{0,1,...,\break r-1\}^{\mathbb N}$. This space can be identified with the interval $[0,1]$ by means of the numeration in base…

Number Theory · Mathematics 2007-05-23 Eric Olivier , Alain Thomas

In the present paper we want to focus on this dichotomy of the non-normal numbers -- on the one hand they are a set of measure zero and on the other hand they are residual -- for dynamical system fulfilling the specification property. These…

Dynamical Systems · Mathematics 2014-03-13 Manfred G. Madritsch , Izabela Petrykiewicz

We prove that for every ergodic invariant measure with positive entropy of a continuous map on a compact metric space there is $\delta>0$ such that the dynamical $\delta$-balls have measure zero. We use this property to prove, for instance,…

Dynamical Systems · Mathematics 2011-10-26 A. Arbieto , C. A. Morales

We construct a natural invariant measure concentrated on the set of square-free numbers, and invariant under the shift. We prove that the corresponding dynamical system is isomorphic to a translation on a compact, Abelian group. This…

Dynamical Systems · Mathematics 2013-04-08 Francesco Cellarosi , Yakov G. Sinai

We consider the soft-core Widom-Rowlinson model for particles with spins and holes, on a Cayley tree of order $d$ (which has $d + 1$ nearest neighbours), depending on repulsion strength $\beta$ between particles of different signs and on an…

Probability · Mathematics 2023-02-14 Sebastian Bergmann , Sascha Kissel , Christof Kuelske

We prove that Poisson measures are invariant under (random) intensity preserving transformations whose finite difference gradient satisfies a cyclic vanishing condition. The proof relies on moment identities of independent interest for…

Probability · Mathematics 2011-02-24 Nicolas Privault

For any transitive piecewise monotonic map for which the set of periodic measures is dense in the set of ergodic invariant measures (such as monotonic mod one transformations and piecewise monotonic maps with two monotonic pieces), we show…

Dynamical Systems · Mathematics 2022-03-30 Yushi Nakano , Kenichiro Yamamoto