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comment Tent map: show that $x$ is a periodic point IFF it is a rational number of the form $\frac {m}{p}$ where $m$ is even and $p$ is odd
@Did: just curious. When you mentioned the fact that "As mentioned before, there is not a whiff of real-analysis in the proof of this result, which boils down to showing that every (2m)/(2n−1) can be written as some k/(2i−1)" who were you talking to? God? If you are commenting on my post directly after I posted it, it is implied you are talking to me. Moreover, you had to trace this post from the other one I made. Stop being a e-bully. Take a chill pill, relax.
Apr
2
accepted Tent map: show that $x$ is a periodic point IFF it is a rational number of the form $\frac {m}{p}$ where $m$ is even and $p$ is odd
Apr
2
comment Tent map: show that $x$ is a periodic point IFF it is a rational number of the form $\frac {m}{p}$ where $m$ is even and $p$ is odd
@Did: I did not yell at you. Do not take usage of syntax to entail tone. I capitalized for I was too lazy to italicize them. I know this is not my page, but the way you were addressing the issue was not conducive to the purposes at hand. If you are less abrasive, may be people will listen to you. Read again what you wrote. Think about what you said. Introspect. You said there is not a whiff of real-analysis in the proof. What do mean by a whiff of real analysis? Moreover dynamical systems pervade almost all aspects of mathematics. I am looking at it from analysis, and I tagged it. Done deal.
Mar
31
comment Tent map: show that $x$ is a periodic point IFF it is a rational number of the form $\frac {m}{p}$ where $m$ is even and $p$ is odd
@julien: Can we do without Euler's function? Also, how did the author arrive at the periodic points being of the form $x- \frac {i}{2^{n-1}}$, for I could not see it. I got $ x- \frac{i}{2^n-1}$. Any ideas on that? I just wish I had a more fleshed out version of it. I can follow the logic, but am failing to produce the algebraic expressions.
Mar
31
comment Tent map: show that $x$ is a periodic point IFF it is a rational number of the form $\frac {m}{p}$ where $m$ is even and $p$ is odd
As I mentioned before, this IS from a real analysis text book which deals slightly with Dynamical Systems. If you have a chauvinist viewpoint of what REAL ANALYSIS is, please keep it to yourself, and I say it very respectfully. I just do not agree with you, and will keep on doing so. So if you would kindly not drop in to every post I make, it will be much appreciated.
Mar
31
asked Tent map: show that $x$ is a periodic point IFF it is a rational number of the form $\frac {m}{p}$ where $m$ is even and $p$ is odd
Mar
30
comment Dynamical Systems problem — a function of ONLY period 3
And there aren't any other periodic points?
Mar
30
comment Dynamical Systems problem — a function of ONLY period 3
Knowing you, I highly doubt the part "of not being able to help"!
Mar
30
comment Dynamical Systems problem — a function of ONLY period 3
Awesome! Also, not related to current problem, I have two other questions posted. Would you mind taking a look at them? math.stackexchange.com/questions/346791/… math.stackexchange.com/questions/346684/…
Mar
30
comment Dynamical Systems problem — a function of ONLY period 3
can I do the following? Let $f(0)= x+1/4$ when $x= 0, 1/4$ and let $f= 0$ for everything else. Won't that work?