Renormalization in the Hénon Family, I: Universality But Non-Rigidity

A ug 2 00 5 RENORMALIZATION IN THE HÉNON FAMILY , I : UNIVERSALITY BUT NON - RIGIDITY

In this paper geometric properties of infinitely renormalizable real Hénon-like maps F in R 2 are studied. It is shown that the appropriately defined renormalizations R n F converge exponentially to the one-dimensional renormalization fixed point. The convergence to one-dimensional systems is at a super-exponential rate controlled by the average Jacobian and a universal function a(x). It is als...

On Family Rigidity Theorems , I Kefeng

Note that Ind(P ) is a virtual G-representation. Let chg(Ind(P )) with g ∈G be the equivariant Chern character of Ind(P ) evaluated at g. In this paper, we first prove a family fixed-point formula that expresses chg(Ind(P )) in terms of the geometric data on the fixed points X of the fiber of π . Then by applying this formula, we generalize the Witten rigidity theorems and several vanishing the...

Combinatorial Models of Rigidity and Renormalization

We first introduce the percolation problems associated with the graph theoretical concepts of (k, l)-sparsity, and make contact with the physical concepts of ordinary and rigidity percolation. We then devise a renormalization transformation for (k, l)-percolation problems, and investigate its domain of validity. In particular, we show that it allows an exact solution of (k, l)-percolation probl...

On Family Rigidity Theorems

Renormalization-group Theory and Universality along the Lambda Line Of

The present status of the renormalization-group (RG) predictions on the superfluid density ρ s and the specific heat C + and C − near the λ-line of 4 He is briefly reviewed. Particular attention is given to universal amplitude ratios related to these quantities. The goals of a new theory project are presented that involves higher-order calculations of the amplitude functions of ρ s , C + and C ...