812,589 research outputs found
Simultaneous dense and nondense orbits for commuting maps
We show that, for two commuting automorphisms of the torus and for two
elements of the Cartan action on compact higher rank homogeneous spaces, many
points have drastically different orbit structures for the two maps.
Specifically, using measure rigidity, we show that the set of points that have
dense orbit under one map and nondense orbit under the second has full
Hausdorff dimension.Comment: 17 pages. Very minor changes to the exposition. Three additional
papers cite
Basis States for Relativistic, Dynamically-Entangled Particles
In several recent papers on entanglement in relativistic quantum systems and
relativistic Bell's inequalities, relativistic Bell-type two-particle states
have been constructed in analogy to non-relativistic states. These
constructions do not have the form suggested by relativistic invariance of the
dynamics. Two relativistic formulations of Bell-type states are shown for
massive particles, one using the standard Wigner spin basis and one using the
helicity basis. The construction hinges on the use of Clebsch-Gordan
coefficients of the Poincar\'e group to reduce the direct product of two
unitary irreducible representations (UIRs) into a direct sum of UIRs.Comment: 19 pages, three tables, revte
Thermodynamic dislocation theory of high-temperature deformation in aluminum and steel
The statistical-thermodynamic dislocation theory developed in previous papers
is used here in an analysis of high-temperature deformation of aluminum and
steel. Using physics-based parameters that we expect theoretically to be
independent of strain rate and temperature, we are able to fit experimental
stress-strain curves for three different strain rates and three different
temperatures for each of these two materials. Our theoretical curves include
yielding transitions at zero strain in agreement with experiment. We find that
thermal softening effects are important even at the lowest temperatures and
smallest strain rates.Comment: 7 pages, 8 figure
Pseudoholomorphic Strips in Symplectisations I: Asymptotic Behavior
This paper is part of a larger program, the investigation of the Chord
Problem in three dimensional contact geometry. The main tool will be
pseudoholomorphic strips in the symplectisation of a three dimensional contact
manifold with two totally real submanifolds as boundary conditions.
The submanifolds and do not intersect transversally. The subject of
this paper is to study the asymptotic behavior of such pseudoholomorphic
strips.Comment: An updated version of the preprint math.SG/0111142 will appear as
four separate papers. This is the first part (53 pages). In this version one
estimate is significantly improve
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