Suppose that A is a C^*-algebra. We consider the class of A-linear mappins between two inner product A-modules such that for each two orthogonal vectors in the domain space their values are orthogonal in the target space. In this paper, we intend to determine A-linear mappings that preserve orthogonality. For this purpose, suppose that E and F are two inner product A-modules and A+ is the set o...

We show the space of expanding Blaschke products on S is compactified by a sphere of invariant measures, reminiscent of the sphere of geodesic currents for a hyperbolic surface. More generally, we develop a dynamical compactification for the Teichmüller space of all measure-preserving topological covering maps of S.

The phase space of an integrable volume-preserving map with one action is foliated by a oneparameter family of invariant tori. Perturbations lead to chaotic dynamics with interesting transport properties. We show that near a rank-one resonant torus the mapping can be reduced to a volume-preserving standard map. This map is a twist map only when the frequency map crosses the resonance curve tran...

For an arbitrary subset I of IR and for a function f defined on I, the number of zeros of f on I will be denoted by ZI(f) . In this paper we attempt to characterize all linear transformations T taking a linear subspace W of C(I) into functions defined on J (I, J ⊆ IR) such that ZI(f) = ZJ (Tf) for all f ∈ W .

We study the critical behavior of period doublings in N symmetrically coupled area-preserving maps for many-coupled cases withN > 3. It is found that the critical scaling behaviors depend on the range of coupling interaction. In the extreme long-range case of global coupling, in which each area-preserving map is coupled to all the other area-preserving maps with equal strength, there exist an i...

Almost every, essentially: Given a Lebesgue measure space (X,B, μ), a property P (x) predicated of elements of X is said to hold for almost every x ∈ X, if the set X \ {x : P (x) holds} has zero measure. Two sets A,B ∈ B are essentially disjoint if μ(A ∩B) = 0. Conservative system: Is an infinite measure preserving system such that for no set A ∈ B with positive measure are A,T−1A,T−2A, . . . p...