Perturbing a product of stable flows

Perturbing a Product of Stable Flows

Suppose that f and f ′ are axiom A flows with attractors A and A′. Then the attractor A×A′ for the product flow gt = ft×f ′ t on the product manifold is no longer hyperbolic (although there is a hyperbolic action of R2). It is easy to see that the attractor cannot explode but we show here that it cannot implode: for any flow (ht) sufficiently close to (gt) any attractor whose basin is not too t...

Relative Compactness and Product Stable Quotient Maps

Stable Flows over Time

In this paper, the notion of stability is extended to network flows over time. As a useful device in our proofs, we present an elegant preflow-push variant of the Gale-Shapley algorithm that operates directly on the given network and computes stable flows in pseudo-polynomial time, both in the static flow and the flow over time case. We show periodical properties of stable flows over time on ne...

Stable Multicommodity Flows

We extend the stable flow model of Fleiner to multicommodity flows. In addition to the preference lists of agents on trading partners for each commodity, every trading pair has a preference list on the commodities that the seller can sell to the buyer. A blocking walk (with respect to a certain commodity) may include saturated arcs, provided that a positive amount of less preferred commodity is...

Product preservation and stable units for reflections into idempotent subvarieties

We give a necessary and sufficient condition for the preservation of finite products by a reflection of a variety of universal algebras into an idempotent subvariety. It is also shown that simple and semi-left-exact reflections into subvarieties of universal algebras are the same. It then follows that a reflection of a variety of universal algebras into an idempotent subvariety has stable units...