Acl and Differentiability of Q-homeomorphisms
نویسنده
چکیده
It is established that a Q-homeomorphism in R, n ≥ 2, is absolute continuous on lines, furthermore, in W 1,1 loc and differentiable a.e. whenever Q ∈ Lloc.
منابع مشابه
On Groups of Diffeomorphisms
I. We consider here the groups of homeomorphisms on Euclidean w-space and the «-sphere Sn. Chiefly we will be concerned with the question of whether or not these groups reduce in an homotopy sense to the ordinary orthogonal group acting on these spaces. Such questions are intimately connected with the theory of fibre bundles in which these spaces occur as fibres. We will restrict ourselves to t...
متن کاملMetric Derived Numbers and Continuous Metric Differentiability via Homeomorphisms
We define the notions of unilateral metric derivatives and “metric derived numbers” in analogy with Dini derivatives (also referred to as “derived numbers”) and establish their basic properties. We also prove that the set of points where a path with values in a metric space with continuous metric derivative is not “metrically differentiable” (in a certain strong sense) is σsymmetrically porous ...
متن کاملA Poincaré Formula for the Fixed Point Indices of the Iterates of Arbitrary Planar Homeomorphisms
Let U ⊂ R2 be an open subset and f : U → R2 be an arbitrary local homeomorphism with Fix f {p}. We compute the fixed point indices of the iterates of f at p, iR2 f, p , and we identify these indices in dynamical terms. Therefore, we obtain a sort of Poincaré index formula without differentiability assumptions. Our techniques apply equally to both orientation preserving and orientation reversing...
متن کاملInvariant measures for quasiperiodically forced circle homeomorphisms
We study quasiperiodically forced circle homeomorphisms and derive a basic classification with respect to the invariant ergodic measures for such systems: Either there exists an invariant graph and every invariant ergodic measure is associated to some invariant graph, or the system is uniquely ergodic. This immediately verifies an observation which is well-known from numerical studies, namely t...
متن کاملMappings of the Sierpinski Curve onto Itself
Given two points p and q of the Sierpinski universal plane curve S, necessary and/ or sufficient conditions are discussed in the paper under which there is a mapping I of S onto itself such that I(P) = q and I belongs to one of the following: homeomorphisms, local homeomorphisms, local homeomorphisms in the large sense, open, simple or monotone mappings.
متن کامل