منابع مشابه
Smooth Deformations of Piecewise Expanding Unimodal Maps
In the space of C piecewise expanding unimodal maps, k ≥ 2, we characterize the C smooth families of maps where the topological dynamics does not change (the “smooth deformations”) as the families tangent to a continuous distribution of codimension-one subspaces (the “horizontal” directions) in that space. Furthermore such codimension-one subspaces are defined as the kernels of an explicit clas...
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In this paper we conjecture that the piecewise linear map f(x) = px1I[0,1/p)(x)+ (sx − s/p)1I[1/p,1](x), p > 1, 0 < s < 1 which has an expanding, onto branch and a contracting branch is eventually piecewise expanding. We give a partial proof of the conjecture, in particular for values of p and s such that d− ln(p(1−s)+s) ln s e 6 = d− ln p ln s e.
متن کاملAlternative Proofs of Linear Response for Piecewise Expanding Unimodal Maps
We give two new proofs that the SRB measure t 7→ μt of a C path ft of unimodal piecewise expanding C maps is differentiable at 0 if ft is tangent to the topological class of f0. The arguments are more conceptual than the one in [4], but require proving Hölder continuity of the infinitesimal conjugacy α (a new result, of independent interest) and using spaces of bounded p-variation. The first ne...
متن کاملLinear Response Formula for Piecewise Expanding Unimodal Maps
The average R(t) = R φdμt of a smooth function φ with respect to the SRB measure μt of a smooth one-parameter family ft of piecewise expanding interval maps is not always Lipschitz [4], [17]. We prove that if ft is tangent to the topological class of f , and if ∂tft|t=0 = X ◦ f , then R(t) is differentiable at zero, and R(0) coincides with the resummation proposed in [4] of the (a priori diverg...
متن کاملExactness and maximal automorphic factors of unimodal interval maps
We study exactness and maximal automorphic factors of C3 unimodal maps of the interval. We show that for a large class of infinitely renormalizable maps, the maximal automorphic factor is an odometer with an ergodic non-singular measure. We give conditions under which maps with absorbing Cantor sets have an irrational rotation on a circle as a maximal automorphic factor, as well as giving exact...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1988
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700027337