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I am asking for the great literature on topics of discrete dynamical systems and/or qualitative theory of difference equations especially aimed on pure mathematicians. Could you please give me some ...

It is clear that one can obtain a discrete dynamical system from a continuous one, but is the converse possible if the system is "nice"? Define the discrete-time dynamical system on $\mathbb{R}^d$ by ...

I solved many cases for the following dynamical system $\dot{x} = x (1-x-ay)$ and $\dot{y} = c y (1- b x -y)$. However, I reached the case where $c>0$ and $a>1$, $b=1$ and I ended up with the ...