A group G is called bounded if every conjugation-invariant norm on has finite diameter. We introduce various strengthenings of this property and investigate them in several classes groups including semisimple Lie groups, arithmetic linear algebraic groups. provide applications to Hamiltonian dynamics.

BIFURCATION SET AND LIMIT CYCLES FORMING COMPOUND EYES IN A PERTURBED HAMILTONIAN SYSTEM JIBIN LI AND ZHENRONG LIU In this paper we consider a class of perturbation of a Hamiltonian cubic system with 9 finite critical points . Using detection functions, we present explicit formulas for the global and local bifurcations of the flow . We exhibit various patterns of compound eyes of limit cycles ....

a graph that contains a hamiltonian cycle is called a hamiltonian graph. in this paper wecompute the first and the second geometric – arithmetic indices of hamiltonian graphs. thenwe apply our results to obtain some bounds for fullerene.

We consider the class of non-Hamiltonian and dissipative statistical systems with distributions that are determined by the Hamiltonian. The distributions are derived analytically as stationary solutions of the Liouville equation for non-Hamiltonian systems. The class of non-Hamiltonian systems can be described by a non-holonomic (non-integrable) constraint: the velocity of the elementary phase ...

AWheeler-Dewitt quantum constraint operator for four-dimensional, non-perturbative Lorentzian vacuum quantum gravity is defined in the continuum. The regulated Wheeler-DeWitt constraint operator is densely defined, does not require any renormalization and the final operator is anomaly-free and at least symmmetric. The technique introduced here can also be used to produce a couple of completely ...