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The Zariski dense orbit conjecture of the arithmetic dynamic is to study the existence of a rational point P with a Zariski dense orbit of a dominant rational self-map f of a projective variety X. Whe...
Groups of automorphisms of trees and their limit sets     Groups  automorphisms  trees  limit sets       font style='font-size:12px;'> 2015/8/26
Let T be a locally finite simplicial tree and let ! ⊂ Aut(T ) be a finitely generated discrete subgroup. We obtain an explicit formula for the critical exponent of the Poincare series associated...
FINITE-ORDER AUTOMORPHISMS OF A CERTAIN TORUS     CERTAIN TORUS  FINITE-ORDER AUTOMORPHISMS       font style='font-size:12px;'> 2015/7/6
Notation. For a positive integer n and a commutative ring R, we write R[n] to denote R Z Z[n] = R[X]=(n), where n denotes the nth cyclotomic polynomial. Thus, for R = Z[n] with n relatively pr...
We show that the automorphism group of Drinfeld's half-space over a finite field is the projective linear group of the underlying vector space. The proof of this result uses analytic geometry in the s...
Given a finitely generated semigroup S of the (normed) set of linear maps of a vector space V into itself, we find sufficient conditions for the exponential growth of the number N(k) of elements of th...
In this paper, we compute universal minimal flows of groups of automorphisms of uncountable $\omega$-homogeneous graphs, $K_n$-free graphs, hypergraphs, partially ordered sets, and their extensions wi...
In this paper, we consider the automorphism groups of the Cayley graph with respect to the Coxeter generators and the Davis complex of an arbitrary Coxeter group. We determine for which Coxeter groups...
Cyclic groups of automorphisms of complex K3 surfaces     Cyclic groups  automorphisms  complex K3 surfaces       font style='font-size:12px;'> 2012/2/29
We determine all possible orders of automorphisms of complex K3 surfaces. A positive integer N is the order of an automorphism of a complex K3 surface if and only if \phi(N) \leq 20 and N is not 60, w...
Let ${mathbb F}_q$ be the finite field of $q$ elements and $k$ be its algebraic closure. Let $Q$ be a quiver with automorphism $sigma$. In this survey we focus on the study of modules over the ${mathb...
Abstract: We study the word length entropy of automorphisms of residually nilpotent groups, and how the entropy of such group automorphisms relates to the entropy of induced automorphisms on various n...
Abstract: We show that if G is a group of automorphisms of a thick finite generalised quadrangle Q acting primitively on both the points and lines of Q, then G is almost simple. Moreover, if G is also...
Abstract: We give an algorithm to determine if the dynamical system generated by a positive automorphism of the free group can also be generated by a self-induced interval exchange transformation. The...
For the simply connected compact exceptional Lie group E8, we determine the structure of subgroup (E8).
For simply connected compact exceptional Lie groups G = F4,E6 and E7, we consider two involutions σ, γ and determine the group structure of subgroups G,of G which are the intersection G ∩ G of the ...
We determine the groups of automorphisms and their orbits for nilpotent Lie algebras of class 2 and small dimension, over arbitrary fields (including the characteristic 2 case).

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