# Tagged Questions

44 views

### Period doubling bifurcation in a quadratic map

I am attempting the find $\mu$ for which the map $$x_{n+1} = \mu + x_n^2$$ undergoes a period doubling bifurcation. I understand that finding the fixed points of the map is the first step towards ...
170 views

### Bounding error when iterating a function

If I am iterating some function $f$ that goes to infinity as x goes to infinity with error $o(g(x))$, for example, is there anyway to bound the error? To be more specific, if I have some sequence ...
329 views

### Why computing Fatou coordinate is so hard?

I'm trying to make images of Fatou coordinate for some polynomial maps. If I'm not wrong there is no explicit general formula/method for computing Fatou coordinate near parabolic fixed point. Is ...
194 views

### Dynamics of the repetitions of $f(z) = z^{2} +\frac{1}{4}$

This is probably a classic and most likely an easy question, but I was not able to find an answer. If we have the iteration $z_{n+1}=g(z_n)$, where $$g(z) = z + a z^{2},$$ with $a\ne 0$, then using a ...
134 views

### Special map $f(x_n)=x_{{n+1} [\mod 4]}$

As mentioned in the headline I am considering the map $f(x_n)=x_{{n+1} [\mod 4]}$. It looks a little bit similar to the dyadic (bernoulli) map but instead of $\mod 1$ we have $\mod 4$ which means that ...
112 views

### How to find periodic solutions using a graphing calculator

We have the model $X_{n+1} = 4\left(X_n - \dfrac{1}{2}\right)^2$ with a given $X_0$ on the domain $[0,1]$. We have the following question: Use your graphing calculator to figure out if there are ...
51 views

### Finding the best real value for $C$.

Consider the recurrence $f_{n+1}=f_n + \ln(f_n)$ with $f_0=2$. Also consider differential equations of type $g(0)=2$ and $\dfrac{d g}{d x}=\ln(g(x)- C \cdot \ln(g(x)))$. Lets call the solution ...
174 views

### An issue with approximations of a recurrence sequence

By trying to give an approximation to a given recurrence sequence I encountered a problem. To be more precise I have a method but it fails if the right condition is not met and I wonder how I should ...