# sinaiMap: Sinai map In nonlinearAnalysis: R package for nonlinear time series analysis

## Description

Generates a 2-dimensional time series using the Sinai map.

## Usage

 ```1 2``` ``` sinaiMap(a = 0.1, start = runif(2), n.sample = 5000, n.transient = 500, do.plot = TRUE) ```

## Arguments

 `start` A 2-dimensional vector indicating the starting values for the x and y Sinai coordinates. If the starting point is not specified, it is generated randomly. `a` The a parameter. Default: 0.1 `n.sample` Length of the generated time series. Default: 5000 samples. `n.transient` Number of transient samples that will be discarded. Default: 500 samples. `do.plot` Logical value. If TRUE (default value), a plot of the generated Sinai system is shown.

## Details

The Sinai map is defined as follows:

x[n+1] = (x[n] + y[n] + a*cos(2*pi*y[n]) )mod 1

y[n+1] = (x[n] + 2*y[n])mod 1

The default selection for the a parameter is known to produce a deterministic chaotic time series.

## Value

A list with two vectors named x and y containing the x-components and the y-components of the Sinai map, respectively.

## Note

Some initial values may lead to an unstable system that will tend to infinity.

## Author(s)

Constantino A. Garcia

## References

Mcsharry, P. E. and P. R. Ruffino (2003). Asymptotic angular stability in nonlinear systems: rotation numbers and winding numbers. Dynamical Systems 18(3), 191-200.

```henon, logisticMap, lorenz, rossler, ikedaMap, cliffordMap, gaussMap```
 ```1 2 3 4 5 6``` ```## Not run: sinai.map = sinaiMap(n.sample = 1000, n.transient=10,do.plot=TRUE) # accessing the x coordinate and plotting it plot(ts(sinai.map\$x)) ## End(Not run) ```