A soft introduction to algebraic entropy
The notion of algebraic entropy of a linear transformation \(\Phi\) on a vector space \(V\) over a field \(K\) is introduced and its basic properties are proved. The definition is given as the supremum on finite dimensional subspaces \(F\) of \(V\) by \(\lim _{n} \dim (F+\Phi F+\dots+\Phi ^{n-1}F)/n\). A characterization of linear transformations with finite algebraic entropy is given. The paper finishes analyzing the notion of adjoint algebraic entropy, also defined by means of dimensions of preimages of subspaces of \(V\) with finite codimension. The adjoint algebraic entropy is proved to be either 0 or infinite.
scientific article; zbMATH DE number 6116566
scientific article