Guest Post: John Rambo fights the Civil War

Today we offer another of our “Guest Post Wednesday” extras, with some meditations on Rambo from Aaron Urbanski. Yeah, we’re not kidding... Rambo. Aaron is a graduate of the GMU American History Masters program and alumnus Ranger of the NPS. [excerpt

Multifractal analysis for conformal graph directed Markov systems

We derive the multifractal analysis of the conformal measure (or equivalently, the invariant measure) associated to a family of weights imposed upon a (multi-dimensional) graph directed Markov system (GDMS) using balls as the filtration. This analysis is done over a large subset of the limit set. In particular, it coincides with the limit set when the GDMS under scrutiny satisfies a boundary separation condition. It also applies to more general situations such as real or complex continued fractions.Comment: 26 page

AV-differential geometry and Newtonian mechanics

A frame independent formulation of analytical mechanics in the Newtonian space-time is presented The differential geometry of affine values i.e., the differential geometry in which affine bundles replace vector bundles and sections of one dimensional affine bundles replace functions on manifolds, is uded. Lagragian and hamiltonian generating objects, together with the Legendre transformation independent on inertial frame are constructed.Comment: Revised and corrected, one subsection added. 16 pages, accepted in ROM

On characterization of Poisson and Jacobi structures

We characterize Poisson and Jacobi structures by means of complete lifts of the corresponding tensors: the lifts have to be related to canonical structures by morphisms of corresponding vector bundles. Similar results hold for generalized Poisson and Jacobi structures (canonical structures) associated with Lie algebroids and Jacobi algebroids.Comment: LaTeX, 14 page