# Tagged Questions

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### There is a horseshoe with positive measure

Here is a theorem by Bowen : My question is about the highlighted part in the picture. why there such a function $g$ exist?
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In Theorem 2.6.4 of Beardon's book, "Iteration of Rational Functions", he states the values for the first two coefficients of an iterated power series. That is, suppose that $$... 1answer 168 views ### Julia sets without Montel's theorem Let J(c) be the Julia set of f(z)=z^2 +c defined as the closure of repelling periodic orbits. Is there a way to prove that J(c) is the boundary of the basin of attraction of attractive fix ... 1answer 164 views ### Approximating an iteratively defined function Let f_0,f_1,\ldots be a sequence of functions f_n : [0,1] \rightarrow R defined as follows:$$f_0(x) =1+2xf_{n}(x) := \left\{\frac{5+t}{2} : \text{ where t solves } ...
Suppose $f$ is a $C^k (1\leq k\leq\infty)$ function from the unit ball $\mathcal{B}$ in $\mathbb{R}^n$ to itself, which is a diffeomorphism from the domain to its image, with the upper and lower ...