Totally Transitive Maps - A Short Note
نویسندگان
چکیده
In this short note we discuss totally transitive maps. We show that all chaotic maps are not necessarily totally transitive, but there are chaotic maps with this property. Our discussion relates to symbol space Σ2 and real line.
منابع مشابه
Transitive Maps Which Are Not Ergodic with Respect to Lebesgue Measure
In this note we shall give examples of rational maps on the Riemann sphere and also of polynomial interval maps which are transitive but not ergodic with respect to Lebesgue measure. In fact, these maps have two disjoint compact attrac-tors whose attractive basins arèintermingled', each having a positive Lebesgue measure in every open set. In addition, we show that there exists a real bi-modal ...
متن کاملOn topological transitive maps on operator algebras
We consider the transitive linear maps on the operator algebra $B(X)$for a separable Banach space $X$. We show if a bounded linear map is norm transitive on $B(X)$,then it must be hypercyclic with strong operator topology. Also we provide a SOT-transitivelinear map without being hypercyclic in the strong operator topology.
متن کاملA Note on Spectrum Preserving Additive Maps on C*-Algebras
Mathieu and Ruddy proved that if be a unital spectral isometry from a unital C*-algebra Aonto a unital type I C*-algebra B whose primitive ideal space is Hausdorff and totallydisconnected, then is Jordan isomorphism. The aim of this note is to show that if be asurjective spectrum preserving additive map, then is a Jordan isomorphism without the extraassumption totally disconnected.
متن کاملA short proof of the maximum conjecture in CR dimension one
In this paper and by means of the extant results in the Tanaka theory, we present a very short proof in the specific case of CR dimension one for Beloshapka's maximum conjecture. Accordingly, we prove that each totally nondegenerate model of CR dimension one and length >= 3 has rigidity. As a result, we observe that the group of CR automorphisms associated with each of such models contains onl...
متن کاملHalf-arc-transitive graphs and chiral hypermaps
A subgroup G of automorphisms of a graph X is said to be 2 -arc-transitive if it is vertexand edgebut not arc-transitive. The graph X is said to be 2 -arc-transitive if Aut X is 1 2 -arc-transitive. The interplay of two different concepts, maps and hypermaps on one side and 2 -arc-transitive group actions on graphs on the other, is investigated. The correspondence between regular maps and 2 -ar...
متن کامل