Chaos in Parabolic Dynamics: Mixing, Rigidity, Spectra

Projektinformationen

CHAPARDYN

ID Finanzhilfevereinbarung: 335989

Abgeschlossenes Projekt

Startdatum 1 Januar 2014

Enddatum 31 August 2019

Finanziert unter

• Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)

Gesamtkosten € 1 193 534,00

EU-Beitrag € 1 193 534,00

Koordiniert durch

UNIVERSITAT ZURICH
Switzerland

Ziel

"The theme of the proposal is the mathematical investigation of chaos (in particular ergodic and spectral properties) in parabolic dynamics, via analytic, geometric and probabilistic techniques. Parabolic dynamical systems are mathematical models of the many phenomena which display a ""slow"" form of chaotic evolution, in the sense that nearby trajectories diverge polynomially in time. In contrast with the hyperbolic case and with the elliptic case, there is no general theory which describes parabolic dynamical systems. Only few classical examples are well understood.

The research plan aims at bridging this gap, by studying new classes of parabolic systems and unexplored properties of classical ones. More precisely, I propose to study parabolic flows beyond the algebraic set-up and infinite measure-preserving parabolic systems, both of which are very virgin fields of research, and to attack open conjectures and questions on fine chaotic properties, such as spectra and rigidity, for area-preserving flows. Moreover, connections between parabolic dynamics and respectively number theory, mathematical physics and probability will be explored. g New techniques, stemming from some recent breakthroughs in Teichmueller dynamics, spectral theory and infinite ergodic theory, will be developed.

The proposed research will bring our knowledge significantly beyond the current state-of-the art, both in breadth and depth and will identify common features and mechanisms for chaos in parabolic systems. Understanding similar features and common geometric mechanisms responsible for mixing, rigidity and spectral properties of parabolic systems will provide important insight towards an universal theory of parabolic dynamics."

Wissenschaftliches Gebiet

• natural sciences › mathematics › applied mathematics › mathematical physics
• natural sciences › mathematics › applied mathematics › dynamical systems
• natural sciences › mathematics › pure mathematics › arithmetics
• natural sciences › mathematics › applied mathematics › mathematical model

Programm/Programme

• FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)

Thema/Themen

• ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations

Aufforderung zur Vorschlagseinreichung

ERC-2013-StG
Andere Projekte für diesen Aufruf anzeigen

Finanzierungsplan

ERC-SG - ERC Starting Grant

Gastgebende Einrichtung

UNIVERSITAT ZURICH

Hauptforscher

Corinna Ulcigrai (Dr.)

Kontakt Verwaltung

Sofia Karakostas (Ms.)

• EU-Beitrag: € 373 362,59
• Adresse: RAMISTRASSE 71 ; 8006 Zurich ; Schweiz
• Region: Schweiz/Suisse/Svizzera › Zürich › Zürich
• Aktivitätstyp: Higher or Secondary Education Establishments
• Gesamtkosten: Keine Daten

Begünstigte (2)

UNIVERSITAT ZURICH

Schweiz

Hauptforscher

Corinna Ulcigrai (Dr.)

Kontakt Verwaltung

Sofia Karakostas (Ms.)

• EU-Beitrag: € 373 362,59
• Adresse: RAMISTRASSE 71 ; 8006 Zurich
• Region: Schweiz/Suisse/Svizzera › Zürich › Zürich
• Aktivitätstyp: Higher or Secondary Education Establishments
• Gesamtkosten: Keine Daten

UNIVERSITY OF BRISTOL

Vereinigtes Königreich

Kontakt Verwaltung

Audrey Michael (Mrs.)

• EU-Beitrag: € 820 171,41
• Adresse: BEACON HOUSE QUEENS ROAD ; BS8 1QU Bristol
• Region: South West (England) › Gloucestershire, Wiltshire and Bristol/Bath area › Bristol, City of
• Aktivitätstyp: Higher or Secondary Education Establishments
• Gesamtkosten: Keine Daten