All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1 Next

Displaying 1 – 20 of 23

Showing per page

A perfect hashing incremental scheme for unranked trees using pseudo-minimal automata

Rafael C. Carrasco, Jan Daciuk (2009)

RAIRO - Theoretical Informatics and Applications

We describe a technique that maps unranked trees to arbitrary hash codes using a bottom-up deterministic tree automaton (DTA). In contrast to other hashing techniques based on automata, our procedure builds a pseudo-minimal DTA for this purpose. A pseudo-minimal automaton may be larger than the minimal one accepting the same language but, in turn, it contains proper elements (states or transitions which are unique) for every input accepted by the automaton. Therefore, pseudo-minimal DTA...

Combinatorial mapping-torus, branched surfaces and free group automorphisms

François Gautero (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We give a characterization of the geometric automorphisms in a certain class of (not necessarily irreducible) free group automorphisms. When the automorphism is geometric, then it is induced by a pseudo-Anosov homeomorphism without interior singularities. An outer free group automorphism is given by a 1 -cocycle of a 2 -complex (a standard dynamical branched surface, see [7] and [9]) the fundamental group of which is the mapping-torus group of the automorphism. A combinatorial construction elucidates...

Discrete anisotropic curvature flow of graphs

Klaus Deckelnick, Gerhard Dziuk (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The evolution of n–dimensional graphs under a weighted curvature flow is approximated by linear finite elements. We obtain optimal error bounds for the normals and the normal velocities of the surfaces in natural norms. Furthermore we prove a global existence result for the continuous problem and present some examples of computed surfaces.

Distributional chaos for flows

Yunhua Zhou (2013)

Czechoslovak Mathematical Journal

Schweizer and Smítal introduced the distributional chaos for continuous maps of the interval in B. Schweizer, J. Smítal, Measures of chaos and a spectral decomposition of dynamical systems on the interval. Trans. Amer. Math. Soc. 344 (1994), 737–854. In this paper, we discuss the distributional chaos DC1–DC3 for flows on compact metric spaces. We prove that both the distributional chaos DC1 and DC2 of a flow are equivalent to the time-1 maps and so some properties of DC1 and DC2 for discrete systems...

Distributional chaos on tree maps: the star case

Jose S. Cánovas (2001)

Commentationes Mathematicae Universitatis Carolinae

Let 𝕏 = { z ∈ ℂ : z n ∈ [ 0 , 1 ] } , n ∈ ℕ , and let f : 𝕏 → 𝕏 be a continuous map having the branching point fixed. We prove that f is distributionally chaotic iff the topological entropy of f is positive.

Existence of quadratic Hubbard trees

Henk Bruin, Alexandra Kaffl, Dierk Schleicher (2009)

Fundamenta Mathematicae

A (quadratic) Hubbard tree is an invariant tree connecting the critical orbit within the Julia set of a postcritically finite (quadratic) polynomial. It is easy to read off the kneading sequences from a quadratic Hubbard tree; the result in this paper handles the converse direction. Not every sequence on two symbols is realized as the kneading sequence of a real or complex quadratic polynomial. Milnor and Thurston classified all real-admissible sequences, and we give a classification of all complex-admissible...

Green functions on self-similar graphs and bounds for the spectrum of the laplacian

Bernhard Krön (2002)

Annales de l’institut Fourier

Combining the study of the simple random walk on graphs, generating functions (especially Green functions), complex dynamics and general complex analysis we introduce a new method for spectral analysis on self-similar graphs.First, for a rather general, axiomatically defined class of self-similar graphs a graph theoretic analogue to the Banach fixed point theorem is proved. The subsequent results hold for a subclass consisting of “symmetrically” self-similar graphs which however is still more general then...

Hubbard trees

Alfredo Poirier (2010)

Fundamenta Mathematicae

We provide a full classification of postcritically finite polynomials as dynamical systems by means of Hubbard trees. The information encoded in these objects is solid enough to allow us recover all the relevant statical and dynamical aspects of the corresponding Julia sets.

Inhomogeneities in non-hyperbolic one-dimensional invariant sets

Brian E. Raines (2004)

Fundamenta Mathematicae

The topology of one-dimensional invariant sets (attractors) is of great interest. R. F. Williams [20] demonstrated that hyperbolic one-dimensional non-wandering sets can be represented as inverse limits of graphs with bonding maps that satisfy certain strong dynamical properties. These spaces have "homogeneous neighborhoods" in the sense that small open sets are homeomorphic to the product of a Cantor set and an arc. In this paper we examine inverse limits of graphs with more complicated bonding...

On local aspects of topological weak mixing in dimension one and beyond

Piotr Oprocha, Guohua Zhang (2011)

Studia Mathematica

We introduce the concept of weakly mixing sets of order n and show that, in contrast to weak mixing of maps, a weakly mixing set of order n does not have to be weakly mixing of order n + 1. Strictly speaking, we construct a minimal invertible dynamical system which contains a non-trivial weakly mixing set of order 2, whereas it does not contain any non-trivial weakly mixing set of order 3. In dimension one this difference is not that much visible, since we prove that every continuous...

On the preservation of combinatorial types for maps on trees

Lluís Alsedà, David Juher, Pere Mumbrú (2005)

Annales de l'institut Fourier

We study the preservation of the periodic orbits of an A -monotone tree map f : T ⟶ T in the class of all tree maps g : S ⟶ S having a cycle with the same pattern as A . We prove that there is a period-preserving injective map from the set of (almost all) periodic orbits of f into the set of periodic orbits of each map in the class. Moreover, the relative positions of the corresponding orbits in the trees T and S (which need not be homeomorphic) are essentially preserved.

On the primary orbits of star maps (second part: spiral orbits)

Lluís Alsedà, José Miguel Moreno (2002)

Applicationes Mathematicae

This paper is the second part of [2] and is devoted to the study of the spiral orbits of self maps of the 4-star with the branching point fixed, completing the characterization of the strongly directed primary orbits for such maps.

Orderings of the rationals and dynamical systems

Claudio Bonanno, Stefano Isola (2009)

Colloquium Mathematicae

This paper is devoted to a systematic study of a class of binary trees encoding the structure of rational numbers both from arithmetic and dynamical point of view. The paper is divided into three parts. The first one is mainly expository and consists in a critical review of rather standard topics such as Stern-Brocot and Farey trees and their connections with continued fraction expansion and the question mark function. In the second part we introduce two classes of (invertible and non-invertible)...

Pruning theory and Thurston's classification of surface homeomorphisms

André de Carvalho, Toby Hall (2001)

Journal of the European Mathematical Society

Two dynamical deformation theories are presented – one for surface homeomorphisms, called pruning, and another for graph endomorphisms, called kneading – both giving conditions under which all of the dynamics in an open set can be destroyed, while leaving the dynamics unchanged elsewhere. The theories are related to each other and to Thurston’s classification of surface homeomorphisms up to isotopy.

Rotation sets for graph maps of degree 1

Lluís Alsedà, Sylvie Ruette (2008)

Annales de l’institut Fourier

For a continuous map on a topological graph containing a loop S it is possible to define the degree (with respect to the loop S ) and, for a map of degree 1 , rotation numbers. We study the rotation set of these maps and the periods of periodic points having a given rotation number. We show that, if the graph has a single loop S then the set of rotation numbers of points in S has some properties similar to the rotation set of a circle map; in particular it is a compact interval and for every rational...

Spaces of ω-limit sets of graph maps

Jie-Hua Mai, Song Shao (2007)

Fundamenta Mathematicae

Let (X,f) be a dynamical system. In general the set of all ω-limit sets of f is not closed in the hyperspace of closed subsets of X. In this paper we study the case when X is a graph, and show that the family of ω-limit sets of a graph map is closed with respect to the Hausdorff metric.

Currently displaying 1 – 20 of 23

Page 1 Next