We give an algebro-geometric approach towards the dynamics of automorphisms/endomorphisms of projective varieties or compact Kähler manifolds, try to determine the building blocks of automorphisms /endomorphisms, and show the relation between the dynamics of automorphisms/endomorphisms and the geometry of the underlying manifolds.

For a substitution satisfying the Pisot, irreducible, unimodular condition, a tiling substitution plays a key role in the construction of Rauzy fractals (see [15, 3]). To try extending techniques developed for substitutions to automorphisms, [6] gives the way to construct Rauzy fractals by using tiling substitutions for automorphisms related to hyperbolic companion matrices of quadratic polynom...

Let G be a group acting on a tree X such that all edge stabilizers are finite. We extend Bestvina-Handel’s theory of train tracks for automorphisms of free groups to automorphisms of G which permute vertex stabilizers. Using this extension we show that there is an upper bound depending only on G for the complexity of the graph of groups decomposition of the fixed subgroups of such automorphisms...

For any field k we fix an algebraic closure of k, denoted by k. For a variety X ⊂ P k we set X = X×k k, we say thatX is smooth ifX is regular, and we let AutX denote the group of k-automorphisms ofX, while LinX denotes the group of linear automorphisms of X , i.e., automorphisms induced by a linear transformation of the coordinates of P. The following theorem was proved by Poonen, see [Po2], Th...

Let be an expansive automorphisms of compact connected abelian group X whose dual group ^ X is cyclic w.r.t. (i.e. ^ X is generated by f n : n 2 Zg for some 2 ^ X). Then there exists a canonical group homomorphism from the spacè 1 (Z;Z) of all bounded two-sided sequences of integers onto X such that = , where is the shift on`1 (Z;Z). We prove that there exists a sooc subshift V ` 1 (Z;Z) such t...

Let be an expansive automorphisms of compact connected abelian group X whose dual group ^ X is cyclic w.r.t. (i.e. ^ X is generated by f n : n 2 Zg for some 2 ^ X). Then there exists a canonical group homomorphism from the spacè 1 (Z;Z) of all bounded two-sided sequences of integers onto X such that = , where is the shift on`1 (Z;Z). We prove that there exists a sooc subshift V ` 1 (Z;Z) such t...