Estimates of global dimension

Dimension Estimates for Invariant Setsof

dedekind modules and dimension of modules

در این پایان نامه، در ابتدا برای مدول ها روی دامنه های پروفر شرایط معادل به دست آورده ایم و خواصی از ددکیند مدول ها روی دامنه های پروفر مشخص کرده ایم. در ادامه برای ددکیند مدول های با تولید متناهی روی حلقه های به طور صحیح بسته شرایط معادل به دست آورده ایم و ددکیند مدول های ضربی را مشخص کرده ایم. گزاره هایی در مورد بعد ددکیند مدول ها بیان کرده ایم. در پایان، قضایای lying over و going down را برا...

Dimension Estimates in Nonconformal Hyperbolic Dynamics

We establish sharp lower and upper estimates for the Hausdorff and box dimensions of invariant sets of maps that need not be conformal nor differentiable. The estimates are given in terms of the geometry of the invariant sets. Our approach is based on the thermodynamic formalism, and uses its nonadditive version. As a byproduct of our approach we give a new characterization of the lower and upp...

G-stable Pieces and Lusztig’s Dimension Estimates

We use G-stable pieces to construct some equidimensional varieties and as a consequence, obtain Lusztig’s dimension estimates [L2, section 4]. This is a generalization of [HL]. In Lemma 1.1 and Proposition 1.2, we assume that G is arbitrary connected algebraic group and G̃ is an algebraic group with identity component G. Lemma 1.1. Let g ∈ G̃. Define i : G̃ → G̃ by i(h) = ghgıhı. For any closed sub...

High frequency dispersive estimates in dimension two

We prove dispersive estimates at high frequency in dimension two for both the wave and the Schrödinger groups for a very large class of real-valued potentials.