166,084 research outputs found
On the class of weakly almost contra-T*-continuous functions
The aim of this paper is to introduce and investigate a new class of
functions called weakly almost contra--continuity which is defined as a
function from an operator topological space into an arbitrary
topological space . Furthermore, some new characterizations,
several basic propositions are proved and some relevant counterexamples are
provided
Hyperbolic Measures on Infinite Dimensional Spaces
Localization and dilation procedures are discussed for infinite dimensional
-concave measures on abstract locally convex spaces (following Borell's
hierarchy of hyperbolic measures).Comment: 25 Page
Topological pressure of simultaneous level sets
Multifractal analysis studies level sets of asymptotically defined quantities
in a topological dynamical system. We consider the topological pressure
function on such level sets, relating it both to the pressure on the entire
phase space and to a conditional variational principle. We use this to recover
information on the topological entropy and Hausdorff dimension of the level
sets.
Our approach is thermodynamic in nature, requiring only existence and
uniqueness of equilibrium states for a dense subspace of potential functions.
Using an idea of Hofbauer, we obtain results for all continuous potentials by
approximating them with functions from this subspace.
This technique allows us to extend a number of previous multifractal results
from the case to the case. We consider ergodic ratios
where the function need not be uniformly positive,
which lets us study dimension spectra for non-uniformly expanding maps. Our
results also cover coarse spectra and level sets corresponding to more general
limiting behaviour.Comment: 32 pages, minor changes based on referee's comment
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