Related papers: Dynamical invariants for group automorphisms
Dynamical degrees and spectra can serve to distinguish birational automorphism groups of varieties in quantitative, as opposed to only qualitative, ways. We introduce and discuss some properties of those degrees and the Cremona degrees,…
In this work we are going to study the dynamics of the linear automorphisms of a measure convolution algebra over a finite group, $T(\mu)=\nu * \mu$. In order to understand an classify the asymptotic behavior of this dynamical system we…
We prove two isomorphism-invariance theorems for groupoids associated with ultragraphs. These theorems characterize ultragraphs for which the topological full group of an associated groupoid is an isomorphism invariant. These results extend…
We develop nilpotently $p$-localization of knot groups in terms of the (symplectic) automorphism groups of free nilpotent groups. We show that any map from the set of conjugacy classes of the outer automorphism groups yields a knot…
In this survey, we discuss a series of linearization problems--for Poisson structures, Lie algebroids, and Lie groupoids. The last problem involves a conjecture on the structure of proper groupoids. Attempting to prove this by the method of…
We introduce a notion of autonomous dynamical systems and apply it to prove rigidity of partially hyperbolic diffeomorphisms on closed compact three-manifolds under some smoothness hypothesis of their associated framing.
We consider periods of automorphic representations of adele groups defined by integrals along Gelfand subgroups. We define natural maps between local components of such periods and construct corresponding global maps using automorphic…
A description of group automorphisms of all two-dimensional algebras, considered up to isomorphism, over any basic field is provided.
In this note we survey recent results on automorphisms of affine algebraic varieties, infinitely transitive group actions and flexibility. We present related constructions and examples, and discuss geometric applications and open problems.
In this note we study the problem of conformally flat structures bounding conformally flat structures and show that the eta invariants give obstructions. These lead us to the definition of an abelian group, the conformal cobordism group,…
In this article we raise some new questions about positive definite functions on free groups, and explain how these are related to more well-known questions. The article is intended as a survey of known results that also offers some new…
We describe the moduli spaces of morphisms between polarized complex abelian varieties. The discrete invariants, derived from a Poincare' decomposition of morphisms, are the types of polarizations and of lattice homomorphisms occurring in…
We introduce the inverse monoid of inner partial automorphisms of a semigroup -- a tool that associates to every semigroup an inverse semigroup. When the semigroup is a group, this inverse semigroup is isomorphic to the group of inner…
We study fixed point sets for holomorphic automorphisms (and endomorphisms) on complex manifolds. The main object of our interest is to determine the number and configuration of fixed points that forces an automorphism (endomorphism) to be…
We present the Hamiltonian formalism for the Euler equation of symplectic fluids, introduce symplectic vorticity, and study related invariants. In particular, this allows one to extend D.Ebin's long-time existence result for geodesics on…
In this survey, we describe recent progress on asymptotic properties of various automorphic orbits in free groups. In particular, we address the problem of counting potentially positive elements of a given length. We also discuss complexity…
This sequel to our previous paper [MS11b] continues the study of topological contact dynamics and applications to contact dynamics and topological dynamics. We provide further evidence that the topological automorphism groups of a contact…
Let G be a complex semisimple linear algebraic group, and X a wonderful G-variety. We determine the connected automorphism group of X and we calculate Luna's invariants of X under its action.
We deform the group of Hamiltonian diffeomorphisms into the group of Hamiltonian automorphisms of a formal star product on a symplectic manifold. We study the geometry of that group and deform the Flux morphism in the framework of…
Twenty years ago Gromov asked about how large is the set of isomorphism classes of groups whose systolic area is bounded from above. This article introduces a new combinatorial invariant for finitely presentable groups called {\it…