We show that a compact, connected set which has uniform oscillations at all points and at all scales has dimension strictly larger than 1. We also show that limit sets of certain Kleinian groups have this property. More generally, we show that if$G$is a non-elementary, analytically finite Kleinian group, and its limit set Λ($G$) is connected, then Λ($G$) is either a circle or has dimension strictly bigger than 1.

No abstract uploaded!

No abstract uploaded!

No abstract uploaded!

We solve the entanglement classification under stochastic local operations and classical communication (SLOCC) for general n-qubit states. For two arbitrary pure n-qubit states connected via local operations, we establish an equation between the two coefficient matrices associated with the states. The rank of the coefficient matrix is preserved under SLOCC and gives rise to a simple way of partitioning all the pure states of n qubits into different families of entanglement classes, as exemplified here. When applied to the symmetric states, this approach reveals that all the Dicke states |l,n> with l=1,..., [n/2] are inequivalent under SLOCC.