Related papers: Sur la dynamique des diff\'eomorphismes birationne…
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…
We introduce and discuss a simple Hamiltonian dynamical system, interpretable as a 3-body problem in the complex plane and providing the prototype of a mechanism explaining the transition from regular to irregular motions as travel on…
Recalling the construction of a flat surface from a Bratteli diagram, this paper considers the dynamics of the shift map on the space of all bi-infinite Bratteli diagrams as the renormalizing dynamics on a moduli space of flat surfaces of…
We make a very detailed analysis of the numerical properties of effective divisors whose support is contained in the exceptional locus of a birational morphism of smooth projective surfaces. As an application we extend Miyaoka's inequality…
This study examines the tree models of mildly dissipative diffeomorphisms on the disk $\D$. These models are one-dimensional dynamical systems with ergodic aperiodic data as well as some properties of the original dynamics. The focus of…
This note provides an insight to the diophantine properties of abelian surfaces with quaternionic multiplication over number fields. We study the fields of definition of the endomorphisms on these abelian varieties and the images of the…
It is known that some equations of differential geometry are derived from variational principle in form of Euler-Lagrange equations. The equations of geodesic flow in Riemannian geometry is an example. Conversely, having Lagrangian…
We prove some general results concerning the size of the group of automorphisms of the Douady space of points on a surface. We then study some properties of the automorphisms coming from an automorphism of the surface, in particular their…
A billiard is a dynamical system in which a particle alternates between motion in a straight line and specular reflection from a boundary. For billiards in non-convex areas bounded by segments of confocal quadrics are studied. The topology…
By complexifying a Hamiltonian system one obtains dynamics on a holomorphic symplectic manifold. To invert this construction we present a theory of real forms which not only recovers the original system but also yields different real…
Smooth real cubic surfaces are birationally trivial (over $\R$) if and only if their real locus is connected or, equivalently, if and only if they have two skew real lines or two skew complex conjugate lines. In such a case a…
We show that in the absence of periodic centre annuli, a partially hyperbolic surface endomorphism is dynamically coherent and leaf conjugate to its linearisation. We proceed to characterise the dynamics in the presence of periodic centre…
We introduce some tools of symbolic dynamics to study the hyperbolic directions of partially hyperbolic diffeomorphisms, emulating the well known methods available for uniformly hyperbolic systems.
We consider random dynamical systems such as groups of conformal transformations with a probability measure, or transversaly conformal foliations with a Laplace operator along the leaves, in which case we consider the holonomy pseudo-group.…
We characterize simple complex abelian varieties and simple abelian surfaces in terms of primitivity of translation automorphisms. Applying this together with a result due to Diller and Favre, we then classify all primitive birational…
The description of invariants of surfaces with respect to the motion groups is reduced to the description of invariants of parameterized surfaces with respect to the motion groups. Existence of a commuting system of invariant partial…
Let X be a real projective algebraic manifold, s numerates connected components of X(R) and _2Br(X) the subgroup of elements of order 2 of the cohomological Brauer group Br(X). We study the natural homomorphism \xi : _2Br(X) \to (Z/2)^s and…
Certain dynamical models of competition have a unique invariant hypersurface to whichevery nonzero tractory is asymptotic, having simple geometry and topology.
Beauville surfaces are a class of complex surfaces defined by letting a finite group $G$ act on a product of Riemann surfaces. These surfaces possess many attractive geometric properties several of which are dictated by properties of the…
A family of algebraic surfaces with many nondegenerate real singularities is introduced with the help of a construction, which has been used in previous works for the generation of substitution tilings.