04/04/2017, 10:52 PM
Well after Some thinking it appears that all multivariable problems reduce to analogues of single variable dynamics , univariate diff equations , delay differential equations and PDE ( partial ( = multivariable ) differential equations.
For instance there are analogue fractals where the half-iteration is not defined.
And analogue Koenig functions.
( if you compute the half-iterate of a random polynomial of degree 2 by using koenigs , you have a problem within the Julia set ( the fractal ) of that polynomial almost surely )
I thank mick and Sheldon for realizing it " completely " now.
Although they did not actively help their past ideas did.
Im not going to define completely here.
There is no reason to assume a multivariable difference equation can be expressed by a univariate difference equation easier or more often than a PDE can be expressed in univar diff equations and vice versa.
Im unaware of a Satisfying formal statement and formal proof of that though.
Regards
Tommy1729
For instance there are analogue fractals where the half-iteration is not defined.
And analogue Koenig functions.
( if you compute the half-iterate of a random polynomial of degree 2 by using koenigs , you have a problem within the Julia set ( the fractal ) of that polynomial almost surely )
I thank mick and Sheldon for realizing it " completely " now.
Although they did not actively help their past ideas did.
Im not going to define completely here.
There is no reason to assume a multivariable difference equation can be expressed by a univariate difference equation easier or more often than a PDE can be expressed in univar diff equations and vice versa.
Im unaware of a Satisfying formal statement and formal proof of that though.
Regards
Tommy1729