6
votes
3answers
324 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 ...
5
votes
2answers
181 views

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

This is probably a classic and maybe easy question, but I was not able to find an answer. If $$g(z) = z + a z^{2},$$ with $a\ne 0$, then using a linear change of coordinates it can be brought to the ...
2
votes
0answers
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 ...
2
votes
1answer
110 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 ...
2
votes
0answers
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 ...
1
vote
1answer
173 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 ...
0
votes
2answers
45 views

Recursive equations critical boundary

I have an interesting problem and i don't have any idea about how to solve it :-) I'm given a system of $K$ equations (with $N \gt K$ , and $0 \lt f \lt 1$) $$f(1-f)^{K-1} - (1-f)^{N-K} \alpha_K = ...
0
votes
1answer
60 views

$Re[f(x + n i)] = 0$ and $f(z)$ is not periodic

Let $z$ be a complex number and $f(z)$ an entire function such that For $x$ real and $n$ any integer. $Re[f(x + n i)] = 0$ and $f(z)$ is not periodic. What are typical examples of such $f(z)$ ? Is ...
0
votes
0answers
332 views

What are the mathematical and “real world” applications of “quadratic maps”, a type of dynamical system?

If we suppose that we can get a generating function for any "quadratic map (as in dynamical systems)", what are the mathematical applications? Also, what are the "real world" applications of this? ...
0
votes
1answer
277 views

Solving Linear Systems with Singular Matrices

Good morning! For (say, homogenous) linear systems of the form $$x_{n+1} = A x_n,$$ where $A$ is a nonsingular matrix, each initial value problem can be solved by the method of finding a general ...
-1
votes
2answers
194 views

Non-numerical method of solving the logistic map

Is there a way to solve a logistic map $$x_{n+1} = kx_n(1-x_n)$$ without using numerical methods/computers? Thanks.
3
votes
2answers
2k views

Linear Algebra: Finding a steady state matrix

Here is the problem: And here is what I tried to do: I tried doing it in my calculator and got that the answer is 40 and 160 as you keep multiplying PX. Can anyone point out what I'm doing wrong ...