Skew Product Attractors and concavity

We propose an approach to the attractors of skew products that tries to avoid unnecessary structures on the base space and rejects the assumption on the invariance of an attractor. When nonivertible maps in the base are allowed, one can encounter the mystery of the vanishing attractor. In the second part of the paper, we show that if the fiber maps are concave interval maps then contraction in the fibers does not depend on the map in the base.