Ebook: Ergodic Theory: with a view towards Number Theory

This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence.

Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits.

Ergodic Theory with a view towards Number Theory will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory.

This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence.

Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits.

Ergodic Theory with a view towards Number Theory will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory.

This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence.

Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits.

Ergodic Theory with a view towards Number Theory will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory.
Content:
Front Matter....Pages I-XVII
Motivation....Pages 1-12
Ergodicity, Recurrence and Mixing....Pages 13-68
Continued Fractions....Pages 69-95
Invariant Measures for Continuous Maps....Pages 97-119
Conditional Measures and Algebras....Pages 121-151
Factors and Joinings....Pages 153-169
Furstenberg's Proof of Szemer?di's Theorem....Pages 171-230
Actions of Locally Compact Groups....Pages 231-275
Geodesic Flow on Quotients of the Hyperbolic Plane....Pages 277-330
Nilrotation....Pages 331-345
More Dynamics on Quotients of the Hyperbolic Plane....Pages 347-402
Back Matter....Pages 403-481

This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence.

Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits.

Ergodic Theory with a view towards Number Theory will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory.
Content:
Front Matter....Pages I-XVII
Motivation....Pages 1-12
Ergodicity, Recurrence and Mixing....Pages 13-68
Continued Fractions....Pages 69-95
Invariant Measures for Continuous Maps....Pages 97-119
Conditional Measures and Algebras....Pages 121-151
Factors and Joinings....Pages 153-169
Furstenberg's Proof of Szemer?di's Theorem....Pages 171-230
Actions of Locally Compact Groups....Pages 231-275
Geodesic Flow on Quotients of the Hyperbolic Plane....Pages 277-330
Nilrotation....Pages 331-345
More Dynamics on Quotients of the Hyperbolic Plane....Pages 347-402
Back Matter....Pages 403-481
....