The behavior of iterations of the intersection body operator in a small neighborhood of the unit ball

Details The behavior of iterations of the intersection body operator in a small neighborhood of the unit ball The behavior of iterations of the intersection body operator in a small neighborhood of the unit ball

2010-03-22

arxiv.org/abs/1003.4056v1

Mathematics

Metric Geometry

12 pages

Scientific paper

The intersection body of a ball is again a ball. So, the unit ball $B_d \subset \R^d$ is a fixed point of the intersection body operator acting on the space of all star-shaped origin symmetric bodies endowed with the Banach-Mazur distance.We show that this fixed point is a local attractor, i.e., that the iterations of the intersection body operator applied to any star-shaped origin symmetric body sufficiently close to $B_d$ in Banach-Mazur distance converge to $B_d$ in Banach-Mazur distance. In particular, it follows that the intersection body operator has no other fixed or periodic points in a small neighborhood of $B_d$.

Affiliated with

Also associated with

No associations

Rating

The behavior of iterations of the intersection body operator in a small neighborhood of the unit ball 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 The behavior of iterations of the intersection body operator in a small neighborhood of the unit ball, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The behavior of iterations of the intersection body operator in a small neighborhood of the unit ball will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-205982