Algebraic entropy and the space of initial values for discrete dynamical systems

Details Algebraic entropy and the space of initial values for discrete dynamical systems Algebraic entropy and the space of initial values for discrete dynamical systems

2001-03-12

arxiv.org/abs/nlin/0103011v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

10 pages, pLatex file

Scientific paper

10.1088/0305-4470/34/48/317

A method to calculate the algebraic entropy of a mapping which can be lifted to an isomorphism of a suitable rational surfaces (the space of initial values) are presented. It is shown that the degree of the $n$th iterate of such a mapping is given by its action on the Picard group of the space of initial values. It is also shown that the degree of the $n$th iterate of every Painlev\'e equation in sakai's list is at most $O(n^2)$ and therefore its algebraic entropy is zero.

Affiliated with

Also associated with

No associations

Rating

Algebraic entropy and the space of initial values for discrete dynamical systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Algebraic entropy and the space of initial values for discrete dynamical systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Algebraic entropy and the space of initial values for discrete dynamical systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-401640