A Nielsen theory for coincidences of iterates

As the title suggests, this paper gives a Nielsen theory of coincidences of iterates of two self maps f, g of a closed manifold. The ideas is, as much as possible, to generalize Nielsen type periodic point theory, but there are many obstacles. Many times we get similar results to the "classical ones" in Nielsen periodic point theory, but with stronger hypotheses.Comment: 30 page

Fibre techniques in Nielsen periodic point theory on nil and solvmanifolds I

AbstractIn this paper and its sequel we give results and methods for evaluating the Nielsen type numbers NΦn(f) and NPn(f) for periodic points of self maps f of nilmanifolds and solvmanifolds (which includes the Klein bottle). Using fibre space techniques we relate these numbers to the various ordinary Nielsen numbers N(fm) of the mth iterate (for m¦n), and thus capitalize on known techniques for our calculations. In this first paper we deal with the specific situation where for each m¦n either N(fm) = R(fm) (the Reidemeister number of fm) or N(fm) = 0. In fact this is the vast majority of cases. In the case where N(fn) = R(fn) we derive the simple formula NΦm(f) = N(fm) for all m¦n

Equivariant coincidence Nielsen numbers

AbstractThe main thrust of this paper is to generalize certain aspects of equivariant Nielsen fixed point theory to coincidences, and to extend both equivariant fixed point, and coincidence point theory so as to include certain types of disconnected fixed point sets. These extensions allow us to exhibit certain important new examples, which enable us to utilize equivariant Nielsen theory in an essential way. In particular in these examples (unlike previous ones), the minimum number of coincidence points cannot be accurately estimated by other existing, or simpler, Nielsen theories. Also new is the inclusion of examples which illustrate the non-abelian side of the story. Finally, we fill a number of gaps and make corrections from earlier expositions in equivariant Nielsen theory

A Nielsen theory for coincidences of iterates

As the title suggests, this paper gives a Nielsen theory of coincidences of iterates of two self maps f, g of a closed manifold. The ideas is, as much as possible, to generalize Nielsen type periodic point theory, but there are many obstacles. Many times we get similar results to the classical ones in Nielsen periodic point theory, but with stronger hypotheses

Lower-rim ferrocenyl substituted calixarenes: new electrochemical sensors for anions

New ferrocene substituted calix[4 and 5]arenes have been prepared and the crystal structure of a lower-rim substituted bis ferrocene calix[4]arene (7) has been elucidated. The respective ferrocene/ferrocenium redox-couples of compounds 6 (a calix[4]arene tetra ferrocene amide) and 8 (a calix[5]arene pentaferrocene amide) are shown to be significantly cathodically perturbed in the presence of anions by up to 160 mV in the presence of dihydrogen phosphate

A model of meta-population dynamics for North Sea and West of Scotland cod - the dynamic consequences of natal fidelity

It is clear from a variety of data that cod (Gadus morhua) in the North Sea do not constitute a homogeneous population that will rapidly redistribute in response to local variability in exploitation. Hence, local exploitation has the potential to deplete local populations, perhaps to the extent that depensation occurs and recovery is impossible without recolonisation from other areas, with consequent loss of genetic diversity. The oceanographic, biological and behavioural processes which maintain the spatial population structures are only partly understood, and one of the key unknown factors is the extent to which codexhibit homing migrations to natal spawning areas. Here, we describe a model comprising 10 interlinked demes of cod in European waters, each representing groups of fish with a common natal origin. The spawning locations of fish in each deme are governed by a variety of rules concerning oceanographic dispersal, migration behaviour and straying. We describe numerical experiments with the model and comparisons with observations, which lead us to conclude that active homing is probably not necessary to explain some of the population structures of European cod. Separation of some sub-populations is possible through distance and oceanographic processes affecting the dispersal of eggs and larvae. However, other evidence suggests that homing may be a necessary behaviour to explain the structure of other sub-populations. Theconsequences for fisheries management of taking into account spatial population structuring are complicated. For example, recovery or recolonisation strategies require consideration not only of mortality rates in the target area for restoration, but also in the source areas for the recruits which may be far removed depending on the oceanography. The model has an inbuilt capability to address issues concerning the effects of climate change, including temperature change, on spatial patterns of recruitment, development and population structure in cod