Objective
REXHALODYN aims at understanding some of the regular and exotic features of Hamiltonian systems, circle maps, and generalized interval exchange transformations, or GIETs. Hamiltonians provide a powerful description of classical mechanics phenomena. Circle maps and GIETs are archetypal examples that illustrate fundamental concepts and phenomena within dynamical systems. Moreover, the latter two offer simplified models that capture essential features of more complex systems; e.g. they appear naturally as Poincar maps of (locally) Hamiltonian flows on compact surfaces, and thus are closely related to Hamiltonians in this context.
Within this framework, the words regular and exotic do not have a precise mathematical meaning; however, we use them here to stand for features in each system that are either well-behaved (regular), such as the existence of stable quasi-periodic motions in Hamiltonian, and rigidity phenomena in circle maps and GIETs; and for features that are ill-behaved (exotic), such as sensitive dependence to initial conditions in Hamiltonians or existence of singular invariant measures in circle maps and GIETs.
Understanding these complementary features deepens our understanding of the systems, their properties, and the underlying mathematical structures that give rise to a rich spectrum of behaviors.
The main objectives of this project are:
-Prove the existence of lower-dimensional invariant tori, associated with a resonant torus with any number of resonances, for general classes (e.g. convex) of near-integrable Hamiltonians.
-Obtain precise estimates for the Hausdorff dimension of the unique invariant probability measure of multicritical circle maps with irrational rotation number of bounded type.
-Obtain rigidity results for multicritical circle maps with irrational rotation number.
The research is planned for two years and takes as a basis many of the results and methods developed by the applicant in his previous works.
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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HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA)
MAIN PROGRAMME
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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.
HORIZON-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships
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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) HORIZON-MSCA-2023-PF-01
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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.
08193 Bellaterra
Spain
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.