We show that for any transcendental meromorphic function f there is a point z in the Julia set of f such that the iterates fn(z) escape, that is, tend to ∞, arbitrarily slowly. The proof uses new covering results for analytic functions. We also introduce several slow escaping sets, in each of which fn(z) tends to ∞ at a bounded rate, and establish the connections between these sets and the Juli...

In computer networking, simulations are widely used to test and analyse new protocols ideas. Currently, there a number of open real testbeds available the protocols. EU, for example, Fed4Fire testbeds, while in US, POWDER COSMOS testbeds. Several other countries, including Japan, Brazil, India, China, have also developed next-generation Compared simulations, these offer more realistic way proto...

We extend results about the dimension of radial Julia set certain exponential functions to quasiregular Zorich maps in higher dimensions. Our improve on previous estimates also special case functions.