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A Brouwer-like theorem for orientation reversing homeomorphisms of the sphere

Marc Bonino (2004)

Fundamenta Mathematicae

We provide a topological proof that each orientation reversing homeomorphism of the 2-sphere which has a point of period k ≥ 3 also has a point of period 2. Moreover if such a k-periodic point can be chosen arbitrarily close to an isolated fixed point o then the same is true for the 2-periodic point. We also strengthen this result by proving that if an orientation reversing homeomorphism h of the sphere has no 2-periodic point then the complement of the fixed point set can be covered by invariant...

A characterization of ω-limit sets for piecewise monotone maps of the interval

Andrew D. Barwell (2010)

Fundamenta Mathematicae

For a piecewise monotone map f on a compact interval I, we characterize the ω-limit sets that are bounded away from the post-critical points of f. If the pre-critical points of f are dense, for example when f is locally eventually onto, and Λ ⊂ I is closed, invariant and contains no post-critical point, then Λ is the ω-limit set of a point in I if and only if Λ is internally chain transitive in the sense of Hirsch, Smith and Zhao; the proof relies upon symbolic dynamics. By identifying points of...

A class of continua that are not attractors of any IFS

Marcin Kulczycki, Magdalena Nowak (2012)

Open Mathematics

This paper presents a sufficient condition for a continuum in ℝn to be embeddable in ℝn in such a way that its image is not an attractor of any iterated function system. An example of a continuum in ℝ2 that is not an attractor of any weak iterated function system is also given.

A class of tridiagonal operators associated to some subshifts

Christian Hernández-Becerra, Benjamín A. Itzá-Ortiz (2016)

Open Mathematics

We consider a class of tridiagonal operators induced by not necessary pseudoergodic biinfinite sequences. Using only elementary techniques we prove that the numerical range of such operators is contained in the convex hull of the union of the numerical ranges of the operators corresponding to the constant biinfinite sequences; whilst the other inclusion is shown to hold when the constant sequences belong to the subshift generated by the given biinfinite sequence. Applying recent results by S. N....

A classification of inverse limit spaces of tent maps with periodic critical points

Lois Kailhofer (2003)

Fundamenta Mathematicae

We work within the one-parameter family of symmetric tent maps, where the slope is the parameter. Given two such tent maps f a , f b with periodic critical points, we show that the inverse limit spaces ( a , f a ) and ( b , g b ) are not homeomorphic when a ≠ b. To obtain our result, we define topological substructures of a composant, called “wrapping points” and “gaps”, and identify properties of these substructures preserved under a homeomorphism.

A Compositional Approach to Synchronize Two Dimensional Networks of Processors

Salvatore La Torre, Margherita Napoli, Mimmo Parente (2010)

RAIRO - Theoretical Informatics and Applications

The problem of synchronizing a network of identical processors that work synchronously at discrete steps is studied. Processors are arranged as an array of m rows and n columns and can exchange each other only one bit of information. We give algorithms which synchronize square arrays of (n × n) processors and give some general constructions to synchronize arrays of (m × n) processors. Algorithms are given to synchronize in time n2, n log n , n n and 2n a square array of (n × n) processors. Our approach...

A Computational Framework to Assess the Efficacy of Cytotoxic Molecules and Vascular Disrupting Agents against Solid Tumours

M. Pons-Salort, B. van der Sanden, A. Juhem, A. Popov, A. Stéphanou (2012)

Mathematical Modelling of Natural Phenomena

A computational framework for testing the effects of cytotoxic molecules, specific to a given phase of the cell cycle, and vascular disrupting agents (VDAs) is presented. The model is based on a cellular automaton to describe tumour cell states transitions from proliferation to death. It is coupled with a model describing the tumour vasculature and its adaptation to the blood rheological constraints when alterations are induced by VDAs treatment....

A contribution to infinite disjoint covering systems

János Barát, Péter P. Varjú (2005)

Journal de Théorie des Nombres de Bordeaux

Let the collection of arithmetic sequences { d i n + b i : n } i I be a disjoint covering system of the integers. We prove that if d i = p k q l for some primes p , q and integers k , l 0 , then there is a j i such that d i | d j . We conjecture that the divisibility result holds for all moduli.A disjoint covering system is called saturated if the sum of the reciprocals of the moduli is equal to 1 . The above conjecture holds for saturated systems with d i such that the product of its prime factors is at most 1254 .

A fixed point theorem for branched covering maps of the plane

Alexander Blokh, Lex Oversteegen (2009)

Fundamenta Mathematicae

It is known that every homeomorphism of the plane which admits an invariant non-separating continuum has a fixed point in the continuum. In this paper we show that any branched covering map of the plane of degree d, |d| ≤ 2, which has an invariant, non-separating continuum Y, either has a fixed point in Y, or is such that Y contains a minimal (in the sense of inclusion among invariant continua), fully invariant, non-separating subcontinuum X. In the latter case, f has to be of degree -2 and X has...

A generalisation of Mahler measure and its application in algebraic dynamical systems

Manfred Einsiedler (1999)

Acta Arithmetica

We prove a generalisation of the entropy formula for certain algebraic d -actions given in [2] and [4]. This formula expresses the entropy as the logarithm of the Mahler measure of a Laurent polynomial in d variables with integral coefficients. We replace the rational integers by the integers in a number field and examine the entropy of the corresponding dynamical system.

A generalization of semiflows on monomials

Hamid Kulosman, Alica Miller (2012)

Mathematica Bohemica

Let K be a field, A = K [ X 1 , , X n ] and 𝕄 the set of monomials of A . It is well known that the set of monomial ideals of A is in a bijective correspondence with the set of all subsemiflows of the 𝕄 -semiflow 𝕄 . We generalize this to the case of term ideals of A = R [ X 1 , , X n ] , where R is a commutative Noetherian ring. A term ideal of A is an ideal of A generated by a family of terms c X 1 μ 1 X n μ n , where c R and μ 1 , , μ n are integers 0 .

A generalization of the self-dual induction to every interval exchange transformation

Sébastien Ferenczi (2014)

Annales de l’institut Fourier

We generalize to all interval exchanges the induction algorithm defined by Ferenczi and Zamboni for a particular class. Each interval exchange corresponds to an infinite path in a graph whose vertices are certain unions of trees we call castle forests. We use it to describe those words obtained by coding trajectories and give an explicit representation of the system by Rokhlin towers. As an application, we build the first known example of a weakly mixing interval exchange outside the hyperelliptic...

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