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- Project's acronym:
- Niezmienniki topologiczne i miary złożoności w działaniu III
- Financial Program Name:
- OPUS
- Organization:
- Narodowe Centrum Nauki (NCN) (National Science Centre)
- Agreement:
- UMO-2014/15/B/ST1/01710 z dnia 2015-07-15
- Realisation period:
- 2015-07-15 - 2018-11-14
- Project manager:
- prof. dr hab. Grzegorz Graff
- Realised in:
- Department of Differential Equations and Mathematical Applications
- Project's value:
- 297 960.00 PLN
- Request type:
- National Research Programmes
- Domestic:
- Domestic project
- Verified by:
- Gdańsk University of Technology
Papers associated with that project
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total: 4
Catalog Projects
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Periodic Points for Sphere Maps Preserving MonopoleFoliations
PublicationLet S^2 be a two-dimensional sphere. We consider two types of its foliations with one singularity and maps f:S^2→S^2 preserving these foliations, more and less regular. We prove that in both cases f has at least |deg(f)| fixed points, where deg(f) is a topological degree of f. In particular, the lower growth rate of the number of fixed points of the iterations of f is at least log|deg(f)|. This confirms the Shub’s conjecture in...
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Detecting coupling directions with transcript mutual information: A comparative study
PublicationCausal relationships are important to understand the dynamics of coupled processes and, moreover, to influence or control the effects by acting on the causes. Among the different approaches to determine cause-effect relationships and, in particular, coupling directions in interacting random or deterministic processes, we focus in this paper on information-theoretic measures. So, we study in the theoretical part the difference between...
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Shub’s conjecture for smooth longitudinal maps of S^m
PublicationLet f be a smooth map of the m-dimensional sphere Sm to itself, preserving the longitudinal foliation. We estimate from below the number of fixed points of the iterates of f , reduce Shub’s conjecture for longitudinal maps to a lower dimensional classical version, and prove the conjecture in case m = 2 and in a weak form for m = 3.
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Generating sequences of Lefschetz numbers of iterates
PublicationDu, Huang and Li showed in 2003 that the class of Dold–Fermat sequences coincides with the class of Newton sequences, which are defined in terms of socalled generating sequences. The sequences of Lefschetz numbers of iterates form an important subclass of Dold–Fermat (thus also Newton) sequences. In this paper we characterize generating sequences of Lefschetz numbers of iterates.
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