Let K be a non-archimedean field, and let φ ∈ K(z) be a rational function of degree d ≥ 2. If φ has potentially good reduction, we give an upper bound, depending only on d, for the minimal degree of an extension L/K such that φ is conjugate over L to a map of good reduction. In particular, if d = 2 or d is less than the residue characteristic of K, the bound is d + 1. If K is discretely valued,...

Every legislature may be defined by a finite integer partition of legislative seats between parties and a winning vote quota defining the minimum coalition size required to pass decisions. In this paper we explore the finite set of integer partitions of legislatures, categorizing all legislatures as one of five basic types. As legislatures approach the partition thresholds between these categor...

References [1] S. Akiyama, T. Borbéli, H. Brunotte, A. Pethö, and J. Thuswaldner. Generalized radix representations and dynamical systems i. Acta Math. Hungarica., 108:207–238, 2005. [2] S. Akiyama, H. Brunotte, A. Pethö, and J. Thuswaldner. Generalized radix representations and dynamical systems ii. Acta Arith., 121:21–61, 2006. [3] S. Akiyama and N Gjini. On the connectedness of self-affine a...

The question of which terms of a recurrence sequence fail to have primitive prime divisors has been significantly studied for several classes of linear recurrence sequences and for elliptic divisibility sequences. In this paper, we consider the question for sequences generated by the iteration of a polynomial. For two classes of polynomials f(x) ∈ Z[x] and initial values a1 ∈ Z, we show that th...

This is a special case of an Artin-Mazur zeta function, which is defined for certain dynamical systems (and in general counts the number of isolated fixed points). Note that we are, as usual, not counting fixed points with multiplicity, which in this case would be something like the Lefschetz index. In fact, if we did count with multiplicity and deg f = d, then |Pern(f)| = d + 1 for all n, and ...

We present an interval arithmetic neural network based on the FIR (Finite Impulse Response) network to improve the prediction power and flexibility. The model for the system is obtained by modifying the dynamics of the FIR network to incorporate the interval arithmetic operations. In this paper, we describe the network architecture and behavior of the interval arithmetic FIR network. We present...

We prove the following mod p version of a case of the dynamical André-Oort conjecture obtained in [GKN ]. Theorem. There are constants c1, c2 depending on d and h such that the following holds. For almost all P, there is a finite subset T ⊂ F̄P , |T | ≤ c1 such that if t ∈ F̄P \ T at least one of the sets { f (`) t (0) : ` = 1, 2, · · · , [c2 logN ] } , { g (`) t (0) : ` = 1, 2, · · · , [c2 logN ...

ABSTRACT. Many analysis and design problems in engineering and science involve uncertainty to varying degrees. This paper is concerned with the structural vibration problem involving uncertain material or geometric parameters, specified as bounds on these parameters. This produces interval parameter values which may be interpreted as interval stiffness and mass matrices. However this approach p...

Notes for a talk in Stanford’s Arithmetic Dynamics Seminar, Apr. 29, 2014. This talk is an introduction to the theory of heights on projective varieties over local and global fields. I will also say something about canonical heights for a dynamical system, and a local-global formula for these. This material is from Chapters 1-2 of the book by Bombieri and Gubler on heights [BG]; also Silverman’...

In this paper we shall study the inverse problem relative to dynamics of the w function which is a special arithmetic function and shall get some results.