Contents 0. Introduction 0.1. Interval exchange maps 0.2. The cohomological equation 0.3. Summary of the contents 1. The continued fraction algorithm for interval exchange maps 1.1. Interval exchange maps 1.2. The continued fraction algorithm 1.3. Roth-type interval exchange maps 2. The cohomological equation 2.1. The theorem of Gottschalk and Hedlund 2.2. Special Birkhoff sums 2.3. Estimates for functions of bounded variation 2.4. Primitives of functions of bounded variation 3. Suspensions of interval exchange maps 3.1. Suspension data 3.2. Construction of a Riemann surface 3.3. Compactification of M∗ 3.4. The cohomological equation for higher smoothness 4. Proof of full measure for Roth type 4.1. The basic operation of the algorithm for suspensions 4.2. The Teichm¨uller flow 4.3. The absolutely continuous invariant measure 4.4. Integrability of log Z(1) 4.5. Conditions (b) and (c) have full measure 4.6. The main step 4.7. Condition (a) has full measure 4.8. Proof of the proposition Appendix A. Roth-type conditions in a concrete family of interval exchange maps Appendix B. A nonuniquely ergodic interval exchange map satisfying condition (a)
The cohomological equation for Roth-type interval exchange maps
MARMI, Stefano;
2005
Abstract
Contents 0. Introduction 0.1. Interval exchange maps 0.2. The cohomological equation 0.3. Summary of the contents 1. The continued fraction algorithm for interval exchange maps 1.1. Interval exchange maps 1.2. The continued fraction algorithm 1.3. Roth-type interval exchange maps 2. The cohomological equation 2.1. The theorem of Gottschalk and Hedlund 2.2. Special Birkhoff sums 2.3. Estimates for functions of bounded variation 2.4. Primitives of functions of bounded variation 3. Suspensions of interval exchange maps 3.1. Suspension data 3.2. Construction of a Riemann surface 3.3. Compactification of M∗ 3.4. The cohomological equation for higher smoothness 4. Proof of full measure for Roth type 4.1. The basic operation of the algorithm for suspensions 4.2. The Teichm¨uller flow 4.3. The absolutely continuous invariant measure 4.4. Integrability of log Z(1) 4.5. Conditions (b) and (c) have full measure 4.6. The main step 4.7. Condition (a) has full measure 4.8. Proof of the proposition Appendix A. Roth-type conditions in a concrete family of interval exchange maps Appendix B. A nonuniquely ergodic interval exchange map satisfying condition (a)File | Dimensione | Formato | |
---|---|---|---|
marmi_moussa_yoccoz_journal_AMS_2005.pdf
Accesso chiuso
Tipologia:
Published version
Licenza:
Non pubblico
Dimensione
495.36 kB
Formato
Adobe PDF
|
495.36 kB | Adobe PDF | Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.