A class of continua that are not attractors of any IFS

This paper presents a sufficient condition for a continuum in $R^n$ to be embeddable in $R^n$ in such a way that its image is not an attractor of any iterated function system. An example of a continuum in $R^2$ that is not an attractor of any weakly contracting iterated function system is also given

On almost specification and average shadowing properties

In this paper we study relations between almost specification property, asymptotic average shadowing property and average shadowing property for dynamical systems on compact metric spaces. We show implications between these properties and relate them to other important notions such as shadowing, transitivity, invariant measures, etc. We provide examples that compactness is a necessary condition for these implications to hold. As a consequence of our methodology we also obtain a proof that limit shadowing in chain transitive systems implies shadowing.Comment: 2 figure

Hadamard's inequality in inner product spaces

Abstract. The aim of this paper is to prove a generalized version of Hadamard’s inequality in inner product spaces with assumptions signifi-cantly weaker than the ones found in existing variants. 1. Introduction. Several different results are known in the literature as Hadamard’s inequal-ity. The most basic version for real square matrices A = [aij]i,j=1,...,n takes the following form

Two results on entropy, chaos, and independence in symbolic dynamics

We survey the connections between entropy, chaos, and independence in topological dynamics. We present extensions of two classical results placing the following notions in the context of symbolic dynamics: 1. Equivalence of positive entropy and the existence of a large (in terms of asymptotic and Shnirelman densities) set of combinatorial independence for shift spaces. 2. Existence of a mixing shift space with a dense set of periodic points with topological entropy zero and without ergodic measure with full support, nor any distributionally chaotic pair. Our proofs are new and yield conclusions stronger than what was known before.Comment: Comments are welcome! This preprint contains results from arXiv:1401.5969v

Dzieci sieci 2.0

S\u142owa kluczowe: kompetencje komunikacyjne m\u142odzie\u17cy, edukacja medialna - gimnazjum, szkolne programy nauczania, netnografia, internet a uczniowie gimnazj\uf3

Dzieci sieci 2.0. Kompetencje komunikacyjne młodych

Monografia, którą oddajemy w Państwa ręce, jest efektem drugiego już projektu badawczego realizowanego pod szyldem Dzieci sieci. Raport to wynik ośmiomiesięcznej pracy dziesięcioosobowego zespołu badaczek i badaczy, którzy zajęli się tematem kompetencji komunikacyjnych związanych z korzystaniem z internetu uczniów na trzecim etapie edukacyjnym. Celem projektu była diagnoza owych umiejętności oraz określenie stanu działań odnoszących się do omawianych kompetencji w zakresie edukacji prowadzonej w ramach formalnego systemu kształcenia. Zadanie Dzieci Sieci – kompetencje komunikacyjne młodych realizował Ośrodek Badań i Analiz Społecznych wspólnie z Instytutem Kultury Miejskiej w Gdańsku, a finansowało Ministerstwo Kultury i Dziedzictwa Narodowego. Omawiany projekt otrzymał dofinansowanie w programie Obserwatorium kultury, a działania badawcze trwały od marca do grudnia 2013 roku. Koordynatorem projektu jest Piotr Siuda, jego asystentem Grzegorz D. Stunża. W skład zespołu badawczego weszli również: Anna Justyna Dąbrowska, Marta Klimowicz, Emanuel Kulczycki, Damian Muszyński, Renata Piotrowska, Ewa Rozkosz, Marcin Sieńko oraz Krzysztof Stachura.Dofinansowano ze środków Ministra Kultury i Dziedzictwa Narodowego

Amorphic complexity can take any nonnegative value in general metric spaces

Amorphic complexity, introduced in 2016, is a new topological invariant of discrete dynamical systems that is of particular interest for systems of entropy zero. Examples exist that show that amorphic complexity can take values 0 and 1 or more (inlcuding infinity), but it was not known if values from the interval (0,1) could be taken. This note proves that for every real nonnegative number there exists a noncomplete metric space and a map on it that has amorphic complexity equal to this number. The construction makes strong use of incompleteness of the space and the question whether these values can be realized for a map on a compact metric space remains open

Measure of minimal sets for certain discrete dynamical systems

AbstractLet X be a separable metric space, μ a complete Borel measure on X that is finite on balls, and f a closed discrete dynamical system on X that preserves μ and has the diameters of all orbits bounded. We prove that almost every point in X (in the sense of measure μ) has its orbit contained in its ω-limit set