Displaying similar documents to “On the dynamics of ϕ : x → x p + a in a local field”

On some issues concerning polynomial cycles

Tadeusz Pezda (2013)

Communications in Mathematics

Similarity:

We consider two issues concerning polynomial cycles. Namely, for a discrete valuation domain R of positive characteristic (for N ≥ 1 ) or for any Dedekind domain R of positive characteristic (but only for N ≥ 2 ), we give a closed formula for a set 𝒞 Y C L ( R , N ) of all possible cycle-lengths for polynomial mappings in R N . Then we give a new property of sets 𝒞 Y C L ( R , 1 ) , which refutes a kind of conjecture posed by W. Narkiewicz.

On the vanishing of Iwasawa invariants of absolutely abelian p-extensions

Gen Yamamoto (2000)

Acta Arithmetica

Similarity:

1. Introduction. Let p be a prime number and ℤ p the ring of p-adic integers. Let k be a finite extension of the rational number field ℚ, k ∞ a ℤ p -extension of k, k n the nth layer of k ∞ / k , and A n the p-Sylow subgroup of the ideal class group of k n . Iwasawa proved the following well-known theorem about the order A n of A n : Theorem A (Iwasawa). Let k ∞ / k be a ℤ p -extension and A n the p-Sylow subgroup of the ideal class group of k n , where k n is the n th layer of k ∞ / k . Then there exist integers λ = λ ( k ∞ / k ) ≥ 0 , μ = μ ( k ∞ / k ) ≥ 0 , ν = ν ( k ∞ / k ) , and n₀ ≥ 0...

On automorphisms of digraphs without symmetric cycles

Piotr Wójcik (1996)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

A digraph is a symmetric cycle if it is symmetric and its underlying graph is a cycle. It is proved that if D is an asymmetric digraph not containing a symmetric cycle, then D remains asymmetric after removing some vertex. It is also showed that each digraph D without a symmetric cycle, whose underlying graph is connected, contains a vertex which is a common fixed point of all automorphisms of D .

Guidance properties of a cylindrical defocusing waveguide

Oldřich John, Charles A. Stuart (1994)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We discuss the propagation of electromagnetic waves of a special form through an inhomogeneous isotropic medium which has a cylindrical symmetry and a nonlinear dielectric response. For the case where this response is of self-focusing type the problem is treated in [1]. Here we continue this study by dealing with a defocusing dielectric response. This tends to inhibit the guidance properties of the medium and so guidance can only be expected provided that the cylindrical stratification...