In this paper, we find the invariant for n-qubits and propose the residual entanglement for n-qubits by means of the invariant. Thus, we establish a relation between SLOCC entanglement and the residual entanglement. The invariant and the residual entanglement can be used for SLOCC entanglement classification for n-qubits. PACS numbers: 03.67.-a, 03.65.Ta, 89.70.+c

In this paper, we find the invariant for n-qubits and propose the residual entanglement for n-qubits by means of the invariant. Thus, we establish a relation between SLOCC entanglement and the residual entanglement. The invariant and the residual entanglement can be used for SLOCC entanglement classification for n-qubits. PACS numbers: 03.67.-a, 03.65.Ta, 89.70.+c

By means of an example it is shown that a supercritical bifurcation of an invariant 2-torus into an invariant 3-torus prevailing in the case of nonresonance may be replaced by a transcritical bifurcation into a pinched invariant 3-torus in the case of resonance. The connections of these bifurcation phenomena with the properties of the spectrum of the underlying invariant 2-torus are discussed. ...

Property (T) for groups means a dichotomy: a representation either has an invariant vector or all vectors are far from being invariant. We show that, under a stronger condition of Żuk, a similar dichotomy holds for almost representations as well.