Project description
Connecting hyperbolic components and wandering domains in complex dynamics
Complex dynamics explores how holomorphic functions evolve when iterated on complex manifolds. Two key concepts in this field are hyperbolic components, which describe stable regions in parameter spaces, and wandering domains – regions that never settle into a repeating pattern. While both are central to the field, their connection remains unclear. With the support of the Marie Skłodowska-Curie Actions programme, the HyCoWanDoCoDyn project aims to link them, focusing on three separate objectives. The first refers to extending the multiplier map to wandering domains. The second involves classifying the structure of Teichmüller spaces associated with these domains, while the third relates to obtaining quasiconformal invariants for their boundary dynamics. Project results could help advance understanding of wandering domains and their role in complex dynamics.
Objective
Complex dynamics is a subfield of dynamical systems, where the systems in question are generated by the iteration of a holomorphic function on a complex manifold. This proposal concerns itself with the following question:
What is the equivalent of a hyperbolic component for parameter families of entire functions with wandering domains?
Both hyperbolicity and wandering domains are the subject of much research in the area, and lie at the core of some of the field's major open questions. This project attempts to link them by focusing on three separate objectives:
- Investigating generalisations to wandering domains of the multiplier map, a central tool in understanding hyperbolic components for parameter families of rational functions.
- Fully classifying the structure of the Teichmüller spaces associated to wandering domains of entire functions.
- Obtaining quasiconformal invariants for the boundary dynamics of wandering domains.
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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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HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA)
MAIN PROGRAMME
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Topic(s)
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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
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) HORIZON-MSCA-2024-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.