Project description
Lyapunov exponents in dynamical systems under study
The Lyapunov exponent was introduced in 1892 to describe the stability of solutions to differential equations. The concept plays a central role in modern theory of dynamical systems, mathematical physics and differential geometry. Funded by the Marie Skłodowska-Curie programme, the main goal of the LYP-RIG project is to study the Lyapunov exponents and investigate their role in rigidity phenomena in dynamical systems. In particular, the project will apply techniques from modern theories of complex analysis and complex geometry. Major focus will be placed on understanding infinite-dimensional hyperbolic symplectic cocycles.
Objective
"This fellowship builds on the success of the applicant’s PhD thesis, where he made breakthroughs in the study of the frequency of hyperbolic behavior, i.e. simplicity and non-vanishing of Lyapunov exponents in dynamical systems. The concept of Lyapunov exponent were introduced in the work of A. M. Lyapunov on the stability of the solutions of differential equations in 1892. The concept plays a central role in most areas of modern theory of dynamical systems, mathematical physics, differential geometry, among others. The problem of the frequency of hyperbolic behavior, in various settings, has been extensively investigated by many leading mathematicians. The main goal of this project is to study the Lyapunov exponents in the most general setting, and investigate its role in rigidity phenomena in dynamical systems. This project specifically aims at applying techniques from modern theories of complex analysis and complex geometry (field in which the supervisor is a world leading expert) to the study of Lyapunov exponents (the applicant’s area of expertise).
This proposal has four main objectives:
1 - Explain the frequency of the simplicity of Lyapunov spectrum for symplectic cocycles;
2 - Establish positivity of Lyapunov exponents for the general structure group;
3 - Understand the frequency of hyperbolic behavior for infinite dimensional ""symplectic"" cocycles;
4 - Employ new techniques from Lyapunov exponents to the rigidity conjectures, in particular, Katok-Spatzier types conjectures."
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics pure mathematics mathematical analysis differential equations
- natural sciences mathematics applied mathematics mathematical physics
- natural sciences mathematics applied mathematics dynamical systems
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics mathematical analysis complex analysis
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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions
MAIN PROGRAMME
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H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility
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Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)
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Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) H2020-MSCA-IF-2018
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
SW7 2AZ London
United Kingdom
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.