Many useful concepts for a quantum theory of scattering and decay (like Lippmann-Schwinger kets, purely outgoing boundary conditions, exponentially decaying Gamow vectors, causality) are not well defined in the mathematical frame set by the conventional (Hilbert space) axioms of quantum mechanics. Using the Lippmann-Schwinger equations as the takeoff point and aiming for a theory that unites re...

Indeed, Margulis [lo] announced that for the geodesic flow on a d-dimensional compact manifold of curvature 1 the number of periodic orbits 7 with (minimal) period r(1) I x is asymptotic to ecd-‘jx/(d 1)x. This result bears a striking resemblance to the prime number theorem. Parry and Pollicott [12], following earlier work by Bowen [2, 41, generalized Margulis’ theorem to weakly mixing Axiom A ...

Over the last 20 years, many of the most spectacular results in the field of dynamical systems dealt specifically with interval and circle maps (or perturbations and complex extensions of such maps). Primarily, this is because in the one-dimensional case, much better distortion control can be obtained than for general dynamical systems. However, many of these spectacular results were obtained s...

We study the spectrum of forcing notions between the iterations of σ-closed followed by ccc forcings and the proper forcings. This includes the hierarchy of α-proper forcings for indecomposable countable ordinals α as well as the Axiom A forcings. We focus on the bounded forcing axioms for the hierarchy of αproper forcings. Following ideas of Shelah we separate them for distinct countable indec...

A diffeomorphism f : M → M on a compact manifold M is partially hyperbolic if there exists a continuous, nontrivial Df -invariant splitting TxM = E s x ⊕ E c x ⊕ E u x , x ∈ M of the tangent bundle such that the derivative is a contraction along E and an expansion along E, with uniform rates, and the behavior of Df along the center bundle E is in between its behaviors along E and E, again by a ...

If the Wholeness Axiom WA0 is itself consistent, then it is consistent with v=hod. A consequence of the proof is that the various Wholeness Axioms are not all equivalent. Additionally, the theory zfc+wa0 is finitely axiomatizable. The Wholeness Axioms, proposed by Paul Corazza, occupy a high place in the upper stratosphere of the large cardinal hierarchy. They are intended as weakenings of the ...

The axiomatic design approach and its two underlying postulates , the independence and the information axiom, introduced by Suh (1990) are based on the fundamental claim that \there are generalizable principles that govern the design process and that these in the form of the design axioms are general principles or self-evident truths that cannot be derived or proven to be true except that there...

We analyze the quasi-stationary distributions of the family of Markov chains {Xε n }, ε > 0, obtained from small non-local random perturbations of iterates of a map f : I → I on a compact interval. The class of maps considered is slightly more general than the class of one-dimensional Axiom A maps. Under certain conditions on the dynamics, we show that as ε → 0 the limit quasi-stationary distri...

Incomplete preferences provide the epistemic foundation for models of imprecise subjective probabilities and utilities that are used in robust Bayesian analysis and in theories of bounded rationality. This paper presents a simple axiomatization of incomplete preferences and characterizes the shape of their representing sets of probabilities and utilities. Deletion of the completeness assumption...

New invariants of 3-dimensional manifolds appearing in the Ktheory of certain operator algebras are introduced. First, we consider the conjugacy problem for pseudo-Anosov diffeomorphisms of a compact surface X. The operator algebra in question is an AF -algebra attached to stable (unstable) foliation of the pseudo-Anosov diffeomorphism. We prove that conjugacy classes of commensurable pseudoAno...