Arnold Seminar at ICTP, Trieste

[Math]

M A T H E M A T I C S   S E M I N A R S   2008


"ARNOLD SEMINAR at ICTP, TRIESTE"


Friday, 15 February, at 14:30 hours


Ricardo Uribe-Vargas
(ICTP, Trieste)

"Arithmetics of the numbers of orbits
of the Fermat-Euler dynamical systems"



Abstract.
Given two positive integers $a, n$, with $(a,n)=1$, we consider
the Fermat-Euler dynamical system $\hat a$, defined by the
multiplication by $a$, acting on the set of residues modulo $n$,  
relatively prime to $n$.

Given an integer $M>1$, the integers $n$ for which the number
of orbits of this dynamical system is a multiple of $M$ form an
ideal in the multiplicative semigroup of odd integers.
We provide new results on the arithmetical properties of these
ideals by using the topological properties of some directed graphs.


The mathematical seminar organised by V.I. Arnold is devoted
to several subjects of mathematics. It takes place on
Fridays, at 14:30 hours, in the Seminar Room of the ICTP Main Building.
Contact: uribe at ictp.it


Venue: SEMINAR ROOM (ICTP Main Building, first floor)