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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Density of orbits and arithmetic degrees of automorphisms of projective threefolds
射影三重 轨道密度 自同构 算术度
2023/4/18
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
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...
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...
Automorphisms of Drinfeld half-spaces over a finite field
Non-archimedean analytic geometry Berkovich spaces Drinfeld upper half-space birational transformations
2012/6/21
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...
Exponential growth of norms in semigroups of linear automorphisms and Hausdorff dimension of self-projective IFS
Exponential growth of norms semigroups of linear automorphisms Hausdorff dimension self-projective IFS Dynamical Systems
2012/4/17
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...
More Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures
Dynamical Systems
2012/4/17
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...
Automorphisms of geometric structures associated to Coxeter groups
Automorphisms geometric structures associated Coxeter groups
2012/3/1
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
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...
Representations of quivers with automorphisms over finite fields
quiver with automorphism hereditary algebra representation
2011/9/28
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...
Entropy of automorphisms, homology and the intrinsic polynomial structure of nilpotent groups
Residually nilpotent group entropy of automorphisms of groups pseudo-Anosov dilatation
2011/9/15
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...
Generalised quadrangles with a group of automorphisms acting primitively on points and lines
Generalised quadrangle primitive permutation group Combinatorics
2011/9/15
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...
Positive automorphisms for self-induced interval exchange transformations
Positive automorphisms self-induced interval exchange transformations Dynamical Systems
2011/9/5
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...
Fixed points subgroups $G^{\sigma,\sigma'}$ by two involutive automorphisms $\sigma$, $\sigma'$ of exceptional compact Lie group $G$, Part II, $G = E_8$
Exceptional Lie group Symmetric space
2011/2/21
For the simply connected compact exceptional Lie group E8, we determine the structure of subgroup (E8).
Fixed points subgroups by two involutive automorphisms $\sigma, \gamma$ of compact exceptional Lie groups $F_4, E_6$ and $E_7$
Fixed points subgroups by two involutive automorphisms $\sigma \gamma$ of compact exceptional Lie groups $F_4, E_6$ $E_7$
2011/2/21
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 ...
Stabilizers of Subspaces under Similitudes of the Klein Quadric, and Automorphisms of Heisenberg Algebras
Klein quadric Grassmann space automorphism orbit nilpotent Lie algebra Heisenberg algebra
2011/1/17
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).