Related papers: Dynamics of Rational Surface Automorphisms: Rotati…

An automorphism of a compact complex space is called wild in the sense of Reichstein--Rogalski--Zhang if there is no non-trivial proper invariant analytic subset. We show that a compact complex surface admitting a wild automorphism must be…

We prove two conjectures on the automorphism group of a one-dimensional formal group law defined over a field of positive characteristic. The first is that if a series commutes with a nontorsion automorphism of the formal group law, then…

We study the dynamics of a generic endomorphism $f$ of an Oka-Stein manifold $X$. Such manifolds include all connected linear algebraic groups and, more generally, all Stein homogeneous spaces of complex Lie groups. We give several…

This paper proposes a new factor rotation for the context of functional principal components analysis. This rotation seeks to re-represent a functional subspace in terms of directions of decreasing smoothness as represented by a generalized…

We develop technics of birational geometry to study automorphisms of affine surfaces admitting many distinct rational fibrations, with a particular focus on the interactions between automorphisms and these fibrations. In particular, we…

We classify real two-dimensional orbits of conformal subgroups such that the orbits contain two circular arcs through a point. Such surfaces must be toric and admit a M\"obius automorphism group of dimension at least two. Our theorem…

We define some pointwise properties of topological dynamical systems and give pointwise conditions for such a system possesses positive topological entropy. We give sufficient conditions to obtain positive topological entropy for maps which…

Let $R$ be a commutative $k-$algebra over a field $k$. Assume $R$ is a noetherian, infinite, integral domain. The group of $k-$automorphisms of $R$,i.e.$Aut_k(R)$ acts in a natural way on $(R-k)$.In the first part of this article, we study…

This paper studies homeomorphisms of surfaces isotopic to the identity by means of purely topological methods and Brouwer theory. The main development is a novel theory of orbit forcing using maximal isotopies and transverse foliations.…

We study multidimensional gravitational models with scalar curvature nonlinearity of the type 1/R and with form-fields (fluxes) as a matter source. It is assumed that the higher dimensional space-time undergoes Freund-Rubin-like spontaneous…

We derive sufficient conditions for a dynamical systems to have a set of irregular points with full topological entropy. Such conditions are verified for some nonuniformly hyperbolic systems such as positive entropy surface diffeomorphisms…

We consider singular holomorphic foliations on compact complex surfaces with invariant rational nodal curve of positive self-intersection. Then, under some assumptions, we list all possible foliations.

Let X be a rational nonsingular compact connected real algebraic surface. Denote by Aut(X) the group of real algebraic automorphisms of X. We show that the group Aut(X) acts n-transitively on X, for all natural integers n. As an application…

We prove the existence of an open and dense set D\subset? Homeo0(T2) (set of toral homeomorphisms homotopic to the identity) such that the rotation set of any element in D is a rational polygon. We also extend this result to the set of…

We prove the Morrison-Kawamata cone conjecture for klt Calabi-Yau pairs in dimension 2. That is, for a large class of rational surfaces as well as K3 surfaces and abelian surfaces, the action of the automorphism group of the surface on the…

We study the groups of automorphisms of rational algebraic surfaces that admit a relatively minimal pencil of curves of arithmetic genus one over an algebraically closed field of arbitrary characteristic. In particular, we classify such…

We show that every automorphism $\alpha$ of a free group $F_k$ of finite rank $k$ has {\it asymptotically periodic} dynamics on $F_k$ and its boundary $\partial F_k$: there exists a positive power $\alpha^q$ such that every element of the…

Suppose that $F$ is a smooth and connected complex surface (not necessarily compact) containing a smooth rational curve $C$ with positive self-intersection. We prove that there exists a neighborhood $U\supset C$ such that any meromorphic…

For every field $k$ of characteristic zero, we determine the groups that act as automorphisms on a smooth cubic surface over $k$. We also determine the groups that act on $k$-rational, stably $k$-rational, or $k$-unirational smooth cubic…

We consider dynamics of the FRW Universe with a scalar field. Using Maupertuis principle we find a curvature of geodesics flow and show that zones of positive curvature exist for all considered types of scalar field potential. Usually,…