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Tree algebra of sofic tree languages

Nathalie Aubrun, Marie-Pierre Béal (2014)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We consider the languages of finite trees called tree-shift languages which are factorial extensible tree languages. These languages are sets of factors of subshifts of infinite trees. We give effective syntactic characterizations of two classes of regular tree-shift languages: the finite type tree languages and the tree languages which are almost of finite type. Each class corresponds to a class of subshifts of trees which is invariant by conjugacy. For this goal, we define a tree algebra which...

Trees and the dynamics of polynomials

Laura G. DeMarco, Curtis T. McMullen (2008)

Annales scientifiques de l'École Normale Supérieure

In this paper we study branched coverings of metrized, simplicial trees F : T → T which arise from polynomial maps f : ℂ → ℂ with disconnected Julia sets. We show that the collection of all such trees, up to scale, forms a contractible space ℙ T D compactifying the moduli space of polynomials of degree D ; that F records the asymptotic behavior of the multipliers of f ; and that any meromorphic family of polynomials over Δ * can be completed by a unique tree at its central fiber. In the cubic case we give a combinatorial...

Trees of visible components in the Mandelbrot set

Virpi Kauko (2000)

Fundamenta Mathematicae

We discuss the tree structures of the sublimbs of the Mandelbrot set M, using internal addresses of hyperbolic components. We find a counterexample to a conjecture by Eike Lau and Dierk Schleicher concerning topological equivalence between different trees of visible components, and give a new proof to a theorem of theirs concerning the periods of hyperbolic components in various trees.

Tube-MPC for a class of uncertain continuous nonlinear systems with application to surge problem

Masoud Taleb Ziabari, Mohammad Reza Jahed-Motlagh, Karim Salahshoor, Amin Ramezani, Ali Moarefianpour (2017)

Kybernetika

This paper presents a new robust adaptive model predictive control for a special class of continuous-time non-linear systems with uncertainty. These systems have bounded disturbances with unknown upper bound, as well as constraints on input states. An adaptive control is used in the new controller to estimate the system uncertainty. Also, to avoid the system disturbances, a H ∞ method is employed to find the appropriate gain in Tube-MPC. Finally, a surge avoidance problem in centrifugal compressors...

Tumour angiogenesis model with variable vessels' effectiveness

Jan Poleszczuk, Iwona Skrzypczak (2011)

Applicationes Mathematicae

We propose a model of vascular tumour growth, which generalises the well recognised model formulated by Hahnfeldt et al. in 1999. Our model is based on the same idea that the carrying capacity for any solid tumour depends on its vessel density but it also incorporates vasculature quality which may be lost during angiogenesis as recognised by Jain in 2005. In the model we assume that the loss of vessel quality affects the diffusion coefficient inside the tumour. We analyse basic mathematical properties...

Turbulent maps and their ω-limit sets

F. Balibrea, C. La Paz (1997)

Annales Polonici Mathematici

One-dimensional turbulent maps can be characterized via their ω-limit sets [1]. We give a direct proof of this characterization and get stronger results, which allows us to obtain some other results on ω-limit sets, which previously were difficult to prove.

Twist systems on the interval

Jozef Bobok (2002)

Fundamenta Mathematicae

Let I be a compact real interval and let f:I → I be continuous. We describe an interval analogy of the irrational circle rotation that occurs as a subsystem of the dynamical system (I,f)-we call it an irrational twist system. Using a coding we show that any irrational twist system is strictly ergodic. We also prove that irrational twist systems exist as subsystems of a large class of systems (I,f) having a cycle of odd period greater than one.

Twisted cotangent sheaves and a Kobayashi-Ochiai theorem for foliations

Andreas Höring (2014)

Annales de l’institut Fourier

Let X be a normal projective variety, and let A be an ample Cartier divisor on X . Suppose that X is not the projective space. We prove that the twisted cotangent sheaf Ω X ⊗ A is generically nef with respect to the polarisation  A . As an application we prove a Kobayashi-Ochiai theorem for foliations: if ℱ ⊊ T X is a foliation such that det ℱ ≡ i ℱ A , then i ℱ is at most the rank of ℱ .

Twisted matings and equipotential gluings

Xavier Buff, Adam L. Epstein, Sarah Koch (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

One crucial tool for studying postcritically finite rational maps is Thurston’s topological characterization of rational maps. This theorem is proved by iterating a holomorphic endomorphism on a certain Teichmüller space. The graph of this endomorphism covers a correspondence on the level of moduli space. In favorable cases, this correspondence is the graph of a map, which can be used to study matings. We illustrate this by way of example: we study the mating of the basilica with itself.

Two commuting maps without common minimal points

Tomasz Downarowicz (2011)

Colloquium Mathematicae

We construct an example of two commuting homeomorphisms S, T of a compact metric space X such that the union of all minimal sets for S is disjoint from the union of all minimal sets for T. In other words, there are no common minimal points. This answers negatively a question posed in [C-L]. We remark that Furstenberg proved the existence of "doubly recurrent" points (see [F]). Not only are these points recurrent under both S and T, but they recur along the same sequence of powers. Our example shows...

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