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J-class abelian semigroups of matrices on ℝn

   | 08. Dez. 2017

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We establish, for finitely generated abelian semigroups G of matrices on ℝn, and by using the extended limit sets (the J-sets), the following equivalence analogous to the complex case: (i) G is hypercyclic, (ii) JG(vη) = ℝn for some vector vη given by the structure of G, (iii) G(vη) = ℝn. This answer a question raised by the author. Moreover we construct for any n = 2 an abelian semigroup G of GL(n, ℝ) generated by n + 1 diagonal matrices which is locally hypercyclic (or J-class) but not hypercyclic and such that JG(ek) = ℝn for every k = 1,…, n, where (e1,…, en) is the canonical basis of ℝn. This gives a negative answer to a question raised by Costakis and Manoussos

eISSN:
2444-8656
Sprache:
Englisch
Zeitrahmen der Veröffentlichung:
2 Hefte pro Jahr
Fachgebiete der Zeitschrift:
Biologie, andere, Mathematik, Angewandte Mathematik, Allgemeines, Physik