How to define an integral for a map from R^2

[funcosed]

Homework Statement

Could someone define the notion of an integral for a map,

x → g(x), x element of R²
or
x_n+1=g(x_n

thanks

 

[Joseph7]

Homework Statement

Could someone define the notion of an integral for a map,

x → g(x), x element of R²
or
x_n+1=g(x_n

thanks

Were you able to find the solution to this problem? Thanks

 

[funcosed]

An integral is a non-constant mapping which remains invarient on the forward orbit i.e. it is a conservative law for the difference equation.