Displaying similar documents to “On some issues concerning polynomial cycles”

On the dynamics of ϕ : x → x p + a in a local field

David Adam, Youssef Fares (2010)

Actes des rencontres du CIRM

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Let K be a local field, a ∈ K and ϕ : x → x p + a where p denotes the characteristic of the residue field. We prove that the minimal subsets of the dynamical system ( K , ϕ ) are cycles and describe the cycles of this system.

Envelopes of holomorphy for solutions of the Laplace and Dirac equations

Martin Kolář (1991)

Commentationes Mathematicae Universitatis Carolinae

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Analytic continuation and domains of holomorphy for solution to the complex Laplace and Dirac equations in 𝐂 n are studied. First, geometric description of envelopes of holomorphy over domains in 𝐄 n is given. In more general case, solutions can be continued by integral formulas using values on a real n - 1 dimensional cycle in 𝐂 n . Sufficient conditions for this being possible are formulated.

On automorphisms of digraphs without symmetric cycles

Piotr Wójcik (1996)

Commentationes Mathematicae Universitatis Carolinae

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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 .