# Tagged Questions

**25**

votes

**2**answers

1k views

### Geometric interpretation of the half-derivative?

For $f(x)=x$, the half-derivative of $f$ is
$$\frac{d^{\frac{1}{2}}}{dx^{\frac{1}{2}}} x = 2 \sqrt{\frac{x}{\pi}} \;.$$
Is there some geometric interpretation of (Q1) this specific derivative, and, ...

**3**

votes

**0**answers

487 views

### Find a second integral for Arnold's example

Consider Arnold's example for Arnold diffusion 1964.
$$H=I_1^2/2+I_2^2/2+\epsilon(1-\cos\theta_2)(1+\mu(\sin\theta_1+\sin t)) $$
We can first make it a system of three degrees of freedom.
Then we ...

**34**

votes

**3**answers

4k views

### On linear independence of exponentials

Problem.
Let $\{\lambda_n\}_{n\in\mathbb N}$ be a sequence of complex numbers . Let's call a family of exponential functions $\{\exp (\lambda_n s)\}_{n\in\mathbb N}$ $F$-independent (where $F$ is ...

**64**

votes

**0**answers

4k views

### Dropping three bodies

Consider the usual three-body problem with Newtonian
$1/r^2$ force between masses. Let the three masses start off at rest,
and not collinear. Then they will become collinear a finite time ...