Periodic points of holomorphic maps via Lefschetz numbers

In this paper we study the set of periods of holomorphic maps on compact manifolds, using the periodic Lefschetz numbers introduced by Dold and Llibre, which can be computed from the homology class of the map. We show that these numbers contain information about the existence of periodic points of a given period; and, if we assume the map to be transversal, then they give us the exact number of such periodic orbits. We apply this result to the complex projective space of dimension n and to some special type of Hopf surfaces, partially characterizing their set of periods. In the first case we also show that any holomorphic map of CP(n) of degree greater than one has infinitely many distinct periodic orbits, hence generalizing a theorem of Fornaess and Sibony. We then characterize the set of periods of a holomorphic map on the Riemann sphere, hence giving an alternative proof of Baker's theorem.

Iowa DOT staff waterway user charge proposal,1976.

The Iowa DOT reviewed Corps of Engineers accounting records to determine the costs of operating and maintaining a 300 mile section of the Mississippi River. This document reviews the details the study.

Tidbits from the Tour Staff, 2007

Tidbits for the Tour Guide Staff that was found in the Senate Journal from 1906.

Tidbits from the Tour Staff, 2007

Tidbits for the Tour Guide Staff that was found in the Senate Journal from March 29, 1917

Tidbits from the Tour Staff, 2007

Tidbits for the Tour Guide Staff that was found in the Journal of the House in 1955

Tidbits from the Tour Staff, 2007

Tidbits for the Tour Guide Staff that was found in the Journal of the Senate, RESOLUTION OF SYMPATHY, March 29, 1917

Tidbits from the Tour Staff, 2007

Tidbits for the Tour Guide Staff that was found in the -- Journal of the House, HOUSE RESOLUTION 6, February 3, 1955

Tidbits from the Tour Staff, 2007

Tidbits for the Tour Guide Staff titled, Iowa and the Nation

Tidbits from the Tour Staff, 2007

Tidbits for the Tour Guide Staff Iowa Senate placed the in the Senate Journal in 1896.

Tidbits from the Tour Staff, 2007

Tidbits for the Tour Guide Staff Clarence Aurner – 1863 - 1948, was an Iowa writer and historian. He has written books and articles detailing Iowa’s early political adventures. The following writing by Clarence Aurner is an account of Iowa’s relocation of the state capital from Iowa City to Des Moines. The story was published originally in the book Iowa Stories, volume 3, by Clarence Ray Aurner, Clio Press, Iowa City, 1917.

Euphorbia L. subsect. Esula (Boiss. in DC.) Pax in the Iberian Peninsula. Leaf surface, chromosome numbers and taxonomic treatment

Presentem l'estudi taxonòmic dels représentants d'Euphorbia subsect. Esula a la Península Ibèrica. Prèviament, s'inclou un primer capítol dedicai a l'estudi de les epidermis foliars i un segon capítol sobre nombres cromosòmics...

Brain Injury Quick Guide: Information and Resources for Teachers and School Staff, July 2013

The Brain Injury Quick Guide was developed as a resource tool for educators and school staff. Functional challenges (including social, physical, communication, and cognitive) are common following brain injury. This booklet serves as a resource outlining common challenges students may face in the classroom as well as strategies for addressing these challenges. Case studies outlining common challenges with possible strategies are provided with suggestions for IEP/504 plan accommodations. Basic brain anatomy and brain injury statistics are also reviewed.

Staff officers manual, 1958

This manual is a compilation of principles, procedures and information to be used as a guide by Iowa Civil Defense Directors, Commanders, Chairmen and their staffs.