Topologically transitive semigroup actions of real linear fractional transformations

Javaheri, Mohammad

doi:10.1016/j.jmaa.2010.03.028

Cited by 10 publications

(12 citation statements)

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“…Hence, every nonnegative rational number appears at most once along the orbit of 0; part (a) of Conjecture 1 simply claims that every nonnegative rational number appears exactly once along the orbit of 0. We have proved in [5] that O a,b is dense for any a, b 1, which in turn implies the following. Theorem 1.3.…”

Section: Introductionmentioning

confidence: 51%

A Collatz-type conjecture on the set of rational numbers

Javaheri¹

2012

Journal of Number Theory

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Let θ(x) = (x − 1)/3 if x 1, and θ(x) = 2x/(1 − x) if 0 x < 1. We conjecture that the θ -orbit of every nonnegative rational number ends in 0. A weaker conjecture asserts that there are no positive rational fixed points for any map in the semigroup Λ generated by the maps 3x + 1 and x/(x + 2). In this paper, we prove that the asymptotic density of the set of maps in Λ that have rational fixed points is zero. Moreover, we prove that certain types of elements in the semigroup Λ cannot have rational fixed points.

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Section: Introductionmentioning

confidence: 51%

A Collatz-type conjecture on the set of rational numbers

Javaheri¹

2012

Journal of Number Theory

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“…Secondly, we prove that the action of any abelian semigroup finitely generated by matrices on K n is never k-transitive for k ≥ 2. This answer a question of Javaheri in ( [7], Problem 3).…”

Section: Introductionmentioning

confidence: 53%

Hypercyclic abelian semigroup of matrices on Cn and Rn and k-transitivity (k ≥ 2)

Ayadi

2013

Appl.Gen.Topol.

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“…Hence we shall prove our main result by studying the set of all hypercyclic points of S U . (1) It is worthy of mentioning that the hypercyclicity of a communicative semigroup generated by finite number of matrices has been extensively studied, for instance, see [13,14,15,16,17] and references therein. In particular, Costakis and Perissis recently proved that there exists a communicative matrix semigroup generated by n + 1 real matrices of Jordan form is hypercylic on R n .…”

Section: The Dynamics Of Matrix Semigroupsmentioning

confidence: 99%