相关论文: Approximate controllability on the group of volume…
There have been various attempts to identify groups of area-preserving diffeomorphisms of 2-dimensional manifolds with limits of SU(N) as $N\to\infty$. We discuss the particularly simple case where the manifold concerned is the…
This is the second article of a sequence of research on deformations of Q-curvature. In the previous one, we studied local stability and rigidity phenomena of Q-curvature. In this article, we mainly investigate the volume comparison with…
We consider theories with time-dependent Hamiltonians which alternate between being bounded and unbounded from below. For appropriate frequencies dynamical stabilization can occur rendering the effective potential of the system stable. We…
For a diffeomorphism which preserves a hyperbolic measure the potential $\phi^u=-\log|{\rm Jac} df|_{E^u}|$ is studied. Various types of pressure of $\phi^u$ are introduced. It is shown that these pressures satisfy a corresponding…
This paper deals with the controllability of the second grade fluids, a class of non-Newtonian of differentiel type, on a two-dimensional torus. Using the method of Agrachev-Sarychev [1], [2] and of Sirikyan [26], we prove that the system…
The geometric nature of Euler fluids has been clearly identified and extensively studied over the years, culminating with Lagrangian and Hamiltonian descriptions of fluid dynamics where the configuration space is defined as the…
We show that within a $C^1$-neighbourhood $\mathcal{U}$ of the set of volume preserving Anosov diffeomorphisms on the three-torus $\mathbb{T}^3$ which are strongly partially hyperbolic with expanding center, any…
We study the normal forms for incompressible flows and maps in the neighborhood of an equilibrium or fixed point with a triple eigenvalue. We prove that when a divergence free vector field in $\mathbb{R}^3$ has nilpotent linearization with…
We prove that the autonomous norm on the group of Hamiltonian diffeomorphisms of the two-dimensional torus is unbounded. We provide explicit examples of Hamiltonian diffeomorphisms with arbitrarily large autonomous norm. For the proofs we…
Several theorems on the volume computing of the polyhedron spanned by a n-dimensional vector set with the finite-interval parameters are presented and proved firstly, and then are used in the analysis of the controllable regions of the…
Invariant tori are prominent features of symplectic and volume preserving maps. From the point of view of chaotic transport the most relevant tori are those that are barriers, and thus have codimension one. For an $n$-dimensional…
This paper is part 1 of a series of papers culminating in the result that measure preserving diffeomorphisms of the disc or 2-torus are unclassifiable. It also addresses another classical problem: which abstract measure preserving systems…
Symmetric spaces arise in wide variety of problems in Mathematics and Physics. They are mostly studied in Representation theory, Harmonic analysis and Differential geometry. As many physical systems have symmetric spaces as their…
In this paper we consider local centralizer classification and rigidity of some toral automorphisms. In low dimensions we classify up to finite index possible centralizers for volume preserving diffeomorphisms $f$ $C^{1}-$close to an…
We are concerned with the problem of global well-posedness of the 3D Navier--Stokes equations on the torus with unitary viscosity. While a full answer to this question seems to be out of reach of the current techniques, we establish a…
In this paper, we seek to combine two emerging standpoints in control theory. On the one hand, recent advances in infinite-dimensional geometric control have unlocked a method for controlling (with arbitrary precision and in arbitrarily…
In this paper we describe the tangent vectors of the stable and unstable manifold of a class of Anosov diffeomorphisms on the torus $\mathbb{T}^2$ using the method of formal series and derivative trees. We start with linear automorphism…
In this paper, we study the control system associated with the incompressible 3D Euler system. We show that the velocity field and pressure of the fluid are exactly controllable in projections by the same finite-dimensional control.…
Rudnick and Wigman (Ann. Henri Poincar\'{e}, 2008; arXiv:math-ph/0702081) conjectured that the variance of the volume of the nodal set of arithmetic random waves on the $d$-dimensional torus is $O(E/\mathcal{N})$, as $E\to\infty$, where $E$…
We construct a Continuous Wavelet Transform (CWT) on the torus $\mathbb T^2$ following a group-theoretical approach based on the conformal group $SO(2,2)$. The Euclidean limit reproduces wavelets on the plane $\mathbb R^2$ with two…