Izvorni znanstveni članak

https://doi.org/10.3336/gm.60.2.07

Uncountable families of fans that admit transitive homeomorphisms

Iztok Banič orcid.org/0000-0002-5097-2903 ; Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška 160, SI-2000 Maribor, Slovenia, Institute of Mathematics, Physics and Mechanics, Jadranska 19, SI-1000 Ljubljana, Slovenia, Andrej Marušič Institute, University of Primorska, Muzejski trg 2, SI-6000 Koper, Slovenia
Goran Erceg orcid.org/0000-0001-8817-4037 ; Faculty of Science, University of Split, Rudera Boškovića 33, 21000 Split, Croatia
Judy Kennedy ; Department of Mathematics, Lamar University, 200 Lucas Building, P.O. Box 10047, Beaumont, Texas 77710, USA
Chris Mouron ; Rhodes College, 2000 North Parkway, Memphis, Tennessee 38112, USA
Van Nall ; Department of Mathematics, University of Richmond, 221 Richmond Way, Richmond, Virginia 23173, USA

Preuzmi JATS datoteku

Sažetak

Recently, we constructed transitive homeomorphisms on the Cantor fan and the Lelek fan. In this paper, we construct a family of uncountably many pairwise non-homeo­morphic smooth fans that admit transitive homeomorphisms. In order to do this, we use our recently developed techniques of combining Mahavier products of closed relations on intervals with quotients of dynamical systems. In addition, we show that the star of Cantor fans admits a transitive homeomorphism. At the end of the paper, we also construct a family of uncountably many pairwise non-homeomorphic non-smooth fans that admit transitive homeomorphisms.

Ključne riječi

Closed relations, Mahavier products, transitive dynamical systems, transitive homeomorphisms, smooth fans, Cantor fans, Lelek fans, stars of Cantor fans

Hrčak ID:

342484

URI

https://hrcak.srce.hr/342484

Datum izdavanja:

9.1.2026.

Posjeta: 399 *