Objective
"Proposal Summary: While there have been tremendous advances in one-dimensional dynamics, higher-dimensional systems are far less well understood. This novel programme of work will take paradigms from one-dimensional dynamics to apply to the higher-dimensional case. In so doing, it will answer a number of long-standing questions of major significance and open up the field for sustained future investigation. The current emphasis on conformal (complex-analytic) techniques will be supplemented in the higher-dimensional setting by drawing on a combination of techniques from dynamics, geometry and analysis.
• Take observations generated by a (possibly chaotic) dynamical system. Do their averages converge? Outcome A will show that for ‘typical’ one-dimensional systems this is indeed the case. This will solve a famous conjecture of Palis and that such maps are stochastically stable.
• Outcome B will rule out certain pathologies in higher-dimensional systems with sufficient regularity. To do this, I will use the one-dimensional paradigm of rigidity associated to smoothness and build on work in progress to deal with the higher dimensionality.
• Specifically, Poincare ́ asked whether recurrent orbits can be shadowed by periodic orbits for a system with nearby parameters. Outcome C will answer his question in a particular setting, using the one- dimensional paradigm of global deformations and higher-dimensional techniques.
• Outcome D will give insight into dynamical systems associated to learning models in economics and game theory – concentrating on models that are either piecewise-affine, have time averages which are essentially piecewise affine, or can be viewed as stochastically perturbed systems. Systems associated to random graphs and coupled networks will also be investigated.
The mathematical methods in these objectives are interlinked, and straddle pure and applied dynamics. This combined approach will greatly re-energise the field."
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: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
- natural sciences mathematics applied mathematics dynamical systems
- medical and health sciences basic medicine pathology
- natural sciences mathematics applied mathematics game theory
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics discrete mathematics graph theory
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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.
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.
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.
ERC-2013-ADG
See other projects for this call
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.
Host institution
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.