In this paper, we present the counterpart of Beckman–Quarles theorem in Poincaré disc model hyperbolic geometry to characterize gyroisometries (hyperbolic isometries) with a single nonzero distance a ∈ 0,1 satisfying id="M2"> <...

We use the intrinsic area to define a distance on space of homothety classes convex bodies in $n$-dimensional Euclidean space, which makes it isometric subset infinite dimensional hyperbolic space. The ambient Lorentzian structure is an extension form bodies, and Alexandrov–Fenchel inequality interpreted as reversed Cauchy–Schwarz inequality. deduce that similarity has proper geodesic with curv...

We study an analytic Hamiltonian system near a strongly resonant periodic orbit. We introduce a modulus of local analytic classification. We provide asymptotic formulae for the exponentially small splitting of separatrices for bifurcating hyperbolic periodic orbits. These formulae confirm a conjecture formulated by V. I. Arnold in the early 1970s.

In this paper we prove the following kind of the unique continuation property. That is the zero on each geodesic of the solution in a real analytic hypersurface for second order anisotropic hyperbolic system with real analytic coefficients can be continued along this curve.