# Tagged Questions

**6**

votes

**1**answer

127 views

### Estimates of Hausdorff dimension (and its derivatives)

For example, the cookie cutter maps, say $T:I_1 \cup I_2 \subset [0,1] \to [0,1] $ is a $C^2$ map such that $|T'|>1$ and provided $I_1$ and $I_2$ are disjoint closed intervals and $T(I_i)=[0,1]$. ...

**6**

votes

**1**answer

179 views

### Approximating an iteratively defined function

Let $f_0,f_1,\ldots$ be a sequence of functions $f_n : [0,1] \rightarrow R$ defined as follows:
$$f_0(x) =1+2x$$
$$f_{n}(x) := \left\{\frac{5+t}{2} : \text{ where t solves } ...

**2**

votes

**0**answers

196 views

### Convergence rate of iterated nonlinear equations?

For $i=1, \dots, n$ ($n$ could be large) we have variables $x_i$ and $y_i$ relating to probability bounds s.t. $x_i, y_i \geq 0, x_i+y_i \leq 1 \; \forall i$. Each $i$ has a constant $\theta_i$, and ...

**3**

votes

**2**answers

218 views

### Convergence rate of an iterative process

I have the following iterative process
$$a_n=a_{n-1}(1-\phi(a_{n-1})),\quad 0< a_0<1,$$
where $\phi(x)$ is a continuous increasing function, $\phi(0)=0$, and if $x\in(0,1)$ then $0< ...

**2**

votes

**0**answers

703 views

### Bessel functions in wave propagation and scattering

Is there a way to scale Bessel J(n,.) (Bessel of first kind) and Bessel H(n,.) (Bessel of third kind or Hankel)? I am having computer problems with higher orders (higher vlaues of n) and small ...

**7**

votes

**1**answer

256 views

### How to estimate the pressure?

I have a finite collection of diffeomorphisms $g_1,\cdots,g_n$ taking the unit interval $I$ to disjoint subintervals $I_1, I_2,\cdots,I_n$. If $G$ is the semigroup they generate, the limit set of $G$ ...

**4**

votes

**5**answers

1k views

### Restricted Three-Body Problem

The movement of a spacecraft between Earth and the Moon is an example of the infamous Three Body Problem. It is said that a general analytical solution for TBP is not known because of the complexity ...

**2**

votes

**2**answers

769 views

### Do the Euler method's approximations always approach the true solution?

Let $B$ be a Banach space and $f : [0,+\infty)\times B \to B$ be a continuous function which is Lipschitz continuous in the second argument with Lipschitz constant $L$ (which does not depend on the ...

**94**

votes

**1**answer

9k views

### What are the shapes of rational functions?

I would like to understand and compute the shapes of rational functions, that is, holomorphic maps of the Riemann sphere to itself, or equivalently, ratios of two polynomials, up to Moebius ...

**7**

votes

**1**answer

961 views

### Area of filled Julia sets

The recent question Area of the boundary of the Mandelbrot set ? prompted me to ask this question.
There has been some work on estimates for the area of the Mandelbrot set, e.g., a paper by John H. ...

**0**

votes

**0**answers

226 views

### What's a good approach to model this system?

Edited 15 Jul 2010
Willie's points are well-taken. I apologize for the wordy description. It turns out have a relative who is quite knowledgeable about numerical problems like this and has offered ...