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What are examples of nonmetrizable attractors?

Metrization theorem

Square (algebra)

Iterated function

Iterated function system

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Examples of nonmetrizable attractors include strange homoclinic attractors and skew-product attractors. Strange homoclinic attractors can contain only one fixed point of saddle type and lead to various scenarios like Lorenz-like and figure-8 attractors, as well as attractors of spiral chaos with different types of fixed points . On the other hand, skew-product attractors are studied in the context of planar diffusively coupled ordinary differential equations, providing a detailed description of their dynamics and Morse decomposition, particularly when certain conditions like asymptotic almost periodicity are met . These examples showcase the diversity and complexity of nonmetrizable attractors in different mathematical systems.

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Journal Article•DOI Structure of non-autonomous attractors for a class of diffusively coupled ODE Alexandre N. Carvalho, Luciano R. N. Rocha, José A. Langa, Rafael Obaya - Show less +3 more 01 Jan 2023 1 Citations	Not addressed in the paper.
Journal Article•DOI An example of noncontinuous attractors Ana Claudia Pereira, Cláudia Buttarello Gentile Moussa, Olímpio H. Miyagaki - Show less +2 more 23 Jul 2015-Journal of Evolution Equations 1 Citations	Examples of nonmetrizable attractors include cases where the lower semicontinuity of equilibrium sets fails at specific points, leading to noncontinuous attractors in certain scenarios.
Journal Article•DOI On scenarios of the onset of homoclinic attractors in three-dimensional non-orientable maps. Alexander Gonchenko, Marina Gonchenko, A. D. Kozlov, E. A. Samylina - Show less +3 more 15 Apr 2021-Chaos 6 Citations	Examples of nonmetrizable attractors include strange homoclinic attractors in three-dimensional non-orientable maps, such as Lorenz-like attractors and figure-8 attractors with saddle fixed points.
Open access•Posted Content•DOI Split square and split carpet as examples of non-metrizable IFS attractors 30 Aug 2022	Examples of non-metrizable attractors include the split square and split carpet, which are defined as compact spaces in the paper by Le Śniak and Nowak.
Journal Article•DOI Split square and split carpet as examples of non-metrizable IFS attractors Krzysztof Le'sniak, Magdalena Nowak - Show less +1 more 30 Aug 2022-Banach Center Publications	Examples of non-metrizable attractors include the split square and split carpet, which are compact spaces defined in the paper as attractors of iterated function systems.

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