Project description
Investigating shadowing property to understand chaotic systems
In the realm of dynamical systems, studying the shadowing property has become a crucial pursuit, providing deep insights into the behaviour of chaotic systems. With the support of the Marie Skłodowska-Curie Actions programme, the TMSHADS project will investigate the shadowing property across three frameworks. Exploringshadowable measures and points will identify the existence of invariant shadowable measures and their role in the existence of odometers, shedding light on the fundamental nature of periodicity in chaotic dynamics. It will delve into the dynamic interplay of hyperbolicity and chaos to understand the implications of shadowing for chaotic systems. It will also explore when the existence of attached singularities forbids a flow from satisfying the shadowing property.
Objective
In the realm of dynamical systems, the study of the Shadowing property has emerged as a pivotal endeavor, offering profound insights into the behavior of chaotic systems. This project delves into the intricacies of the Shadowing property across three distinct frameworks: Shadowable Measures and Points, CW-hyperbolic Homeomorphisms, and Singular Flows, each with their unique characteristics and challenges. With a focus on these disparate contexts, our investigation aims to unravel the implications of shadowing for the chaotic nature of such systems, while also unraveling the obstructions that arise in continuous time cases.
Our exploration into Shadowable Measures and Points harnesses we seeks the existence of invariant shadowable measures and their role in the existence of odometers, shedding light on the fundamental nature of periodicity in chaotic dynamics. In the domain of CW-hyperbolic Homeomorphisms, we navigate the dynamic interplay of hyperbolicity and chaos. Our focus extends to investigating periodic shadowing, periodic specification, measures of maximal entropy, and the discovery of new examples that contribute to the broader landscape of chaotic systems theory. Furthermore, our investigation extends to Singular Flows, where we confront the nuanced challenges presented by singularities in continuous time dynamics. We investigate when the existence of attached singularities forbids a flow to satisfy the shadowing property. This exploration not only advances our understanding of continuous-time systems but also evidences a remarkable difference between the discrete-time and continuous-time contexts.
Fields of science (EuroSciVoc)
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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.
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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)
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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)
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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
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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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(opens in new window) HORIZON-MSCA-2023-PF-01
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30-059 Krakow
Poland
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