Related papers: Typical infinite mixing automorphisms are rank-one

In paper [1] S. V. Tikhonov introduced a complete metric on the space of mixing transformations. It generates a topology called leash-topology. In [2] Tikhonov states the following problem: for what mixing transformation T its conjugacy…

J.-P. Thouvenot and the author showed via different approaches that the centralizer of a mixing rank-one infinite measure preserving transformation was trivial. In this note the author presents his joining proof. We also consider…

A survey article that presents some recent algebraic and model-theoretic results on the automorphism groups of relatively free groups of infinite rank. The topics include topological aspects, generating sets, descripition of automorpisms…

In the present paper, we show that many combinatorial and topological objects, such as maps, hypermaps, three-dimensional pavings, constellations and branched coverings of the two--sphere admit any given finite automorphism group. This…

We present mixing ergodic automorphisms of a space with sigma-finite measure whose symmetric tensor squares have simple spectra. This property is of interest in connection with dynamical spectral problems of A.N. Kolmogorov and V.A.…

We study dynamical properties of automorphisms of compact nilmanifolds and prove that every ergodic automorphism is exponentially mixing and exponentially mixing of higher orders. This allows to establish probabilistic limit theorems and…

Recently, Shestakov-Umirbaev solved Nagata's conjecture on an automorphism of a polynomial ring. To solve the conjecture, they defined notions called reductions of types I--IV for automorphisms of a polynomial ring. An automorphism…

We examine properties of generic automorphisms of the random poset, with the goal of explicitly characterizing them. We associate to each automorphism an auxiliary first-order structure, consisting of the random poset equipped with an…

We give a fairly complete characterization of the exact components of a large class of uniformly expanding Markov maps of $\mathbb{R}$. Using this result, for a class of $\mathbb{Z}$-invariant maps and finite modifications thereof, we prove…

1. We answer Michael Gordin's question providing singular spectrum for transformations with homoclinic Bernoulli flows via Poisson suspensions induced by modified Sidon rank-one constructions. 2. We give homoclinic proof of Emmanuel Roy's…

We prove mixing on a general class of rank-one transformations containing all known examples of rank-one mixing, including staircase transformations and Ornstein's constructions, and a variety of new constructions.

We prove that every finite group is the automorphism group of a finite abstract polytope isomorphic to a face-to-face tessellation of a sphere by topological copies of convex polytopes. We also show that this abstract polytope may be…

This paper exploits adjacencies between the orbits of an ordered set P and a consequence of the classification of finite simple groups to, in many cases, exponentially bound the number of automorphisms. Results clearly identify the…

For a class of irrational numbers, depending on their Diophantine properties, we construct explicit rank-one transformations that are totally ergodic and not weakly mixing. We classify when the measure is finite or infinite. In the finite…

We show that the sequence of dimensions of the linear spaces, generated by a given rank-metric code together with itself under several applications of a field automorphism, is an invariant for the whole equivalence class of the code. These…

The present work investigates regular, semiregular, and chiral polytopes of any rank $d\geq 3$, whose automorphism groups are 2-groups. There is a large variety of rather small finite regular or alternating semiregular polytopes with…

We offer a criterion for showing that the automorphism group of an ultrahomogeneous structure is topologically 2-generated and even has a cyclically dense conjugacy class. We then show how finite topological rank of the automorphism group…

Padberg introduced a geometric notion of ranks for (mixed) integer rational polyhedrons and conjectured that the geometric rank of the matching polytope is one. In this work, we prove that this conjecture is true.

We prove for residually finite groups the following long standing conjecture: the number of twisted conjugacy classes of an automorphism of a finitely generated group is equal (if it is finite) to the number of finite dimensional…

We show that generic automorphisms of stable groups are supertight in a strong sense. In particular, we obtain the existence of supertight automorphisms. We also answer a question concerning the relationship between supertight automorphisms…