All Questions

Label $X$ as the real interval $[0, a]$ where $a \in \mathbb{R}^+$, so that $\text{int}(X) = (0, a)$ labels the interior of $X$ and $\partial X$ labels the boundary of $X$. I have a function $f:\text{...

Let $(X,d)$ be a metric space and $f:X\rightarrow X$ be continuous. Then, is there any meaning/research done on the metric $$ D(x,y)\triangleq \sum_{n \in \mathbb{N}} \frac1{2^n} d(f^n(x),f^n(y)); $$ ...

Let $\Phi$ be a homeomorphism of a compact metric space $M$ which preserves a regular Borel probability measure $\mu$.(`Regular' $\mu(U) > 0$, if U open. ) Under these hypothesis, I have two ...