In this paper we prove that all the hyperbolic components of the family λ tan z except the punctured unit disk are simply connected. Then, restricting λ to the imaginary axis, We show that there is a “Sharkovskii-like” ordering of the periods of the hyperbolic components. Finally, again for λ in the imaginary axis, we show that period doubling phenomena occur.

It is known that there are only finitely many imaginary abelian number fields with class numbers equal to their genus class numbers. Here, we determine all the imaginary cyclic fields of 2-power degrees with class numbers equal to their genus class numbers.

For a non-square transfer matrix with zeros on the extended imaginary axis including infinity, this paper discusses how to dilate (augment) such transfer matrix to a square one without adding extra zeros on the extended imaginary axis. The state-space construction for the dilation is proposed by using the finite and infinite eigenstructures of the transfer matrix. Copyright c © 2002 IFAC

We classify irreducible Whittaker modules for generalized Heisenberg Lie algebra t and irreducible Whittaker modules for Lie algebra t̃ obtained by adjoining m degree derivations d1, d2, . . . , dm to t. Using these results, we construct imaginary Whittaker modules for non-twisted extended affine Lie algebras and prove that the imaginary Whittaker modules of Z-independent level are always irredu...