Orbits of uniform dimension.

Uniform distribution of orbits of lattices

Bifurcations of Periodic Orbits and Uniform Approximations

We derive uniform approximations for contributions to Gutzwiller’s periodic-orbit sum for the spectral density which are valid close to bifurcations of periodic orbits in systems with mixed phase space. There, orbits lie close together and give collective contributions, while the individual contributions of Gutzwiller’s type would diverge at the bifurcation. New results for the tangent, the per...

Entropy, Dimension and Uniform Distribution

The starting point for this work is an old question of H. Furstenberg. Recall that a Borel probability measure on the torus T = R=Z is called p-invariant if p = , where p(x) def = p x (mod 1) and p def = 1 p . Suppose that is non-atomic, and is simultaneously 2and 3-invariant. Assume also that is ergodic under the joint action of 2; 3. Does it follow that is necessarily Lebesgue measure? In his...

On the VC-dimension of uniform hypergraphs

Let F be a k-uniform hypergraph on [n] where k − 1 is a power of some prime p and n ≥ n0(k). Our main result says that if |F | > ( n k−1 ) − logp n + k!kk , then there exists E0 ∈ F such that {E ∩ E0 : E ∈ F} contains all subsets of E0. This improves a longstanding bound of ( n k−1 ) due to Frankl and Pach [7].

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...