Richard Evan Schwartz, Brown University, Providence, RI.

• IntroductionPart 1: Some other polygon iterationsA primer on projective geometryElementary algebraic geometryThe pentagram mapSome related dynamical systemsPart 2: The projective heat mapTopological degree of the mapThe convex caseThe basic domainsThe method of positive dominanceThe Cantor setTowards the quasi horseshoeThe quasi horseshoePart 3: Sketches for the remaining resultsTowards the solenoidThe solenoidLocal structure of the Julia setThe embedded graphConnectedness of the Julia setTerms, formulas, and coordinate listingsReferences

Richard Evan Schwartz, Brown University, Providence, RI.

• IntroductionPart 1: Some other polygon iterationsA primer on projective geometryElementary algebraic geometryThe pentagram mapSome related dynamical systemsPart 2: The projective heat mapTopological degree of the mapThe convex caseThe basic domainsThe method of positive dominanceThe Cantor setTowards the quasi horseshoeThe quasi horseshoePart 3: Sketches for the remaining resultsTowards the solenoidThe solenoidLocal structure of the Julia setThe embedded graphConnectedness of the Julia setTerms, formulas, and coordinate listingsReferences

Richard Evan Schwartz, Brown University, Providence, RI.

• IntroductionPart 1: Some other polygon iterationsA primer on projective geometryElementary algebraic geometryThe pentagram mapSome related dynamical systemsPart 2: The projective heat mapTopological degree of the mapThe convex caseThe basic domainsThe method of positive dominanceThe Cantor setTowards the quasi horseshoeThe quasi horseshoePart 3: Sketches for the remaining resultsTowards the solenoidThe solenoidLocal structure of the Julia setThe embedded graphConnectedness of the Julia setTerms, formulas, and coordinate listingsReferences