Exponential map (discrete dynamical systems)

Family

The family of exponential functions is called the exponential family.

Forms

There are many forms of these maps, many of which are equivalent under a coordinate transformation. For example two of the most common ones are:

The second one can be mapped to the first using the fact that λ ∗ e z . = e z + l n ( λ ) , so E λ : z → e z + l n ( λ ) is the same under the transformation z = z + l n ( λ ) . The only difference is that, due to multi-valued properties of exponentiation, there may be a few select cases that can only be found in one version. Similar arguments can be made for many other formulas.