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- W1985753727 abstract "AbstractWe will consider a convex subset of a metric linear space and a certain group of actions G on this set, that allow us to define the notion of Haar zero measure on sets that have zero Haar measure for the translation (by adding) invariant HSY prevalence theory. In this way, we will be able to define the meaning of G-prevalent set according to the pioneering work of Christensen. Our setting considers problems which take into account the convex structure and this is quite different from the previous results on prevalence which consider basically the linear additive structure. In this setting, we will show a kind of quantitative Kupka–Smale theorem, and also we generalize a result about rotation numbers which was first considered by J.-C. Yoccoz (and, also by M. Tsujii). Among other things we present an estimation of the amount of hyperbolicity in a setting that we believe was not considered before.Keywords: prevalentquantitative Kupka–Smalediffeomorphisms of the circlegroup of actionstranslation invariant AcknowledgementsA.O. Lopes is partially supported by CNPq, PRONEX – Sistemas Dinâmicos, INCT, and beneficiary of CAPES financial support. E.R. Oliveira is partially supported by CNPq.Notes1. Probabilities on TM which minimizes the integral ∫TML(v, v)dμ(x, v) under a suitable holonomic condition.2. One can see that H = (1 − t)F + tG is uniformly bounded by , where δ = min {cF, cG}." @default.
- W1985753727 created "2016-06-24" @default.
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- W1985753727 date "2014-09-11" @default.
- W1985753727 modified "2023-10-11" @default.
- W1985753727 title "On generic<i>G</i>-prevalent properties and a quantitative K-S theorem for<i>C</i><sup><i>r</i></sup>diffeomorphisms of the circle" @default.
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- W1985753727 doi "https://doi.org/10.1080/14689367.2014.951599" @default.
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