library(expm)

## Loading required package: Matrix
## 
## Attaching package: 'expm'
## 
## The following object is masked from 'package:Matrix':
## 
##     expm

Definimos el integrando de la función \(I(t)\).

I <- function(x){
          sin(2*x)*exp(sin(x)+cos(x))
      }

Cálculo de \(I(2\pi)\).

I <- integrate(I,0,2*pi)

Matriz \(\Phi(2\pi)\).

phi = matrix(c(1,I$value/exp(1),0,1),2,2,byrow=TRUE)
phi

##      [,1]      [,2]
## [1,]    1 0.6803986
## [2,]    0 1.0000000

Matriz de constante

L=logm(phi)/(2*pi)
L

##      [,1]      [,2]
## [1,]    0 0.1082888
## [2,]    0 0.0000000

Exponentes de Floquet

eigen(L)$value

## [1] 0 0

Multiplicadores de Floquet

eigen(phi)$value

## [1] 1 1