Grant: Alliance Grants
Queen's University
$100,000.00
Anosov Dynamics
FY 2024-25
Summary
The goal of the present research is to understand better, and fully classify, a type of dynamical systems called Anosov and Pseudo-Anosov flows. Anosov flows are paradigmatic examples of chaotic dynamical systems, i.e., those systems where an arbitrarily small difference in initial condition leads to a large deviance in the behavior of the orbit, as popularized in the "butterfly effect". As such, understanding chaotic systems in general, and Anosov flows in particular, has been an important goal in the field of dynamical systems since at least the 1960s.
In this proposal, we aim to tackle some of the biggest open questions surrounding pseudo-Anosov flows, such as obtaining a complete classification of these systems, understanding precisely which manifolds can carry such flows, and determining whether or not a given manifold can carry infinitely many non-equivalent pseudo-Anosov flows.
Program
Alliance Grants
Recipient
Location
Ontario, Canada
Recipient Type
Academia
Type
Grant
Source
NSERC's Awards Data
As published
Application id
598447-2024
Name nom
Barthelme, Thomas T
Department département
Mathematics and Statistics
Organization id
29
Institution établissement
Queen's University
Province en
Ontario
Province fr
Ontario
Country en
CANADA
Country fr
CANADA
Fiscal year exercice financier
2024
Competition year année de concours
2024
Award amount
100000
Program id
ALLRP
Program name en
Alliance Grants
Program name fr
Subventions Alliance
Group en
RESEARCH PARTNERSHIPS
Group fr
PARTENARIATS DE RECHERCHE
Committee code
96
Committee name en
RPP Internal Decision Cttee
Committee name fr
Cté de décision interne - PPR
Area of application code
1200
Area of application group en
Advancement of knowledge
Area of application group fr
Avancement des connaissances
Area of application en
Advancement of knowledge
Area of application fr
Avancement des connaissances
Research subject code
2900
Research subject group en
Pure mathematics
Research subject group fr
Mathématiques pures
Research subject en
Pure mathematics
Research subject fr
Mathématiques pures
Field of research list names en
Not available
Field of research list names fr
Non disponible
Socioeconomic objective list names en
Not available
Socioeconomic objective list names fr
Non disponible
Application title
Anosov Dynamics
Keywords
3-manifold topology; geometric topology; hyperbolic dynamics; pseudo-anosov flows; topological dynamical systems
Application summary
The goal of the present research is to understand better, and fully classify, a type of dynamical systems called Anosov and Pseudo-Anosov flows. Anosov flows are paradigmatic examples of chaotic dynamical systems, i.e., those systems where an arbitrarily small difference in initial condition leads to a large deviance in the behavior of the orbit, as popularized in the "butterfly effect". As such, understanding chaotic systems in general, and Anosov flows in particular, has been an important goal in the field of dynamical systems since at least the 1960s.
In this proposal, we aim to tackle some of the biggest open questions surrounding pseudo-Anosov flows, such as obtaining a complete classification of these systems, understanding precisely which manifolds can carry such flows, and determining whether or not a given manifold can carry infinitely many non-equivalent pseudo-Anosov flows.
