Georgia Institute of Technology College of Sciences

"Shadowing" in dynamical systems is the property that an approximate orbit (satisfying some additional properties) can be followed closely by a true orbit. This is a basic tool to construct complicated orbits since construction of approximate orbits is sometimes easier. It is also important in applications since numerical computations produce only approximate orbits and it requires an extra argument to show that the approximate ofbit produced by the computer corresponds to a real orbit. There are three standard mechanicsms for shadowing: Hyperbolicity, topological methods, shadowing of minimizers. We will present hyperbolicity.