Translating Symbolic

For an extensive explanation of the problem, see the explanation.

Installing

Get it via cargo.

cargo install translating-symbolic

To install cargo, run

curl --proto '=https' --tlsv1.2 -sSf https://sh.rustup.rs | sh

Executing

If installed via cargo, execute the command translating-symbolic.

Otherwise, you can run the program by executing cargo run in the root of this repository.

Usage

The program will read input from stdin. Type in a symbolic sequence in the following format:

LR or L1R2 or LRLRLRLR or L10R20. Whitespace is ignored.

On Enter, the symbolic sequence of the same cycle in the full model is displayed. This may be two coexisting cycles.

Ctrl-D stops the program.

Explanation

Suppose the model function $f$ of your dynamical system is a circle map and piecewise-smooth. It is defined on some domain $[0, 2n]$ and has four branches $f_A, f_B, f_C,$ and $f_D$. Suppose additionally, it has the following symmetry:

$$f(x + n) \equiv f(x) + n \mod 2n$$

This model is referred to as the full model. The model function of the halved model is a circle map $h$, that is defined on the domain $[0, n]$ and

$$h(x) = f(x) \quad \forall \in [0, n]$$

It has only two branches that are called $L$ and $R$.

This program translates the symbolic sequences of a cycle in the halved model to its symbolic sequence in the full model.