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This question may be easy; however, I have been unable to locate any references regarding the specific scenario described below. Let $T:[0,1]\to [0,1]$ be the quadratic map $T(x) = 3.83 x (1-x)$. It i …

This question was previously posted on MSE. Let $M, N$ be smooth connected manifolds (without boundary), where $M$ is a compact manifold, so we can put a topology in the space $\mathcal C^\infty(M, N) …

I'm studying the structural stability of vector fields and I'm interested in learning about this phenomenon on compact $2$-manifolds with boundary. Let $M^2$ be a compact connected 2-manifold and $\ …

(This question was previously posted on MSE and I decided to post it here too.) Let $f:\mathbb{R}\times \mathbb{R}^n \to \mathbb{R}$ be a smooth function, such that $$f(0,0)=0,\ \frac{\partial f}{\pa …

Context and Definitions Consider the interval $I=[0,1]$. We say that $T:I\to I$ satisfies the axiom A (I am following [1]) if: $T$ has a finite number of hyperbolic periodic attractors; and defining …

Let $X$ be a compact Hausdorff topological space, and $\mathcal C^0 (X) = \{f:X\to\mathbb{R}; \ f \text{ is continuous }\}$. It is well known that for any bounded linear functional $\phi: \mathcal C^ …