Accession Number:

ADA210257

Title:

An Introduction to Fractals and Chaos

Descriptive Note:

Final rept. Jun 1988-1989

Corporate Author:

AIR FORCE ACADEMY COLORADO SPRINGS CO

Personal Author(s):

Report Date:

1989-06-01

Pagination or Media Count:

174.0

Abstract:

Fractals and chaos have gained immense popularity in the last few years. Fractal objects and chaotic dynamics are being postulated and observed in diverse areas of science. This report gives a mathematical introduction to fractals and chaos, including some necessary background for the technical definitions. Partial Contents Fractal -- Observations and representations Topology and open covers Topological dimension Hausdorff dimension A definition of fractal Similarity dimension The Cantor set Koch snowflakes Random coastlines Another approach - IFS Iterated Function System and Further examples Chaos -- The Poincare map Iterations of continuous functions -- Orbits Periodic points Invariant setsAttractors Scrambled Sets -- Definitions of chaos Universality -- The bifurcation diagram Higher dimensions Complex dynamics and Randomness. EDC

Subject Categories:

  • Theoretical Mathematics
  • Computer Programming and Software

Distribution Statement:

APPROVED FOR PUBLIC RELEASE