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Parrondo´s paradox for homeomorphisms

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dc.contributor.authorGasull, A.
dc.contributor.authorHernández Corbato, Luis
dc.contributor.authorRuiz del Portal, Francisco R.
dc.date.accessioned2023-06-17T08:28:33Z
dc.date.available2023-06-17T08:28:33Z
dc.date.issued2021-06-16
dc.description.abstractWe construct two planar homeomorphisms f and g for which the origin is a globally asymptotically stable fixed point whereas for f ◦ g and g ◦ f the origin is a global repeller. Furthermore, the origin remains a global repeller for the iterated function system generated by f and g where each of the maps appears with a certain probability. This planar construction is also extended to any dimension greater than 2 and proves for first time the appearance of the Parrondo’s dynamical paradox in odd dimensions.
dc.description.departmentDepto. de Álgebra, Geometría y Topología
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedFALSE
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/73470
dc.identifier.doi10.1017/prm.2021.28
dc.identifier.issn0308-2105
dc.identifier.officialurlhttps://doi.org/10.1017/prm.2021.28
dc.identifier.urihttps://hdl.handle.net/20.500.14352/7231
dc.journal.titleProceedings of the Royal Society of Edinburgh. Section A: Mathematics
dc.language.isoeng
dc.publisherCambridge University Press
dc.rightsAtribución 3.0 España
dc.rights.accessRightsopen access
dc.rights.urihttps://creativecommons.org/licenses/by/3.0/es/
dc.subject.cdu514
dc.subject.keywordFixed points
dc.subject.keywordLocal and global asymptotic stability
dc.subject.keywordParrondo’s dynamical paradox
dc.subject.keywordRandom dynamical system
dc.subject.ucmMatemáticas (Matemáticas)
dc.subject.ucmGeometría
dc.subject.unesco12 Matemáticas
dc.subject.unesco1204 Geometría
dc.titleParrondo´s paradox for homeomorphisms
dc.typejournal article
dcterms.references[1] R. B. Ash. Real analysis and probability. Probability and Mathematical Statistics, No. 11. Academic Press, New York-London, 1972. [2] P. Billingsley. Probability and measure. Third edition. Wiley Series in Probability and Mathematical Sta�tistics. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1995. [3] V. D. Blondel, J. Theys, J. N. Tsitsiklis.When is a pair of matrices stable?. In: V. D. Blondel, A. Megretski (eds.). Unsolved problems in Mathematical Systems and Control Theory. Princeton Univ. Press, NJ 2004. [4] J. S. C´anovas, A. Linero, D. Peralta-Salas. Dynamic Parrondo’s paradox. Physica D 218 (2006) 177–184. [5] A. Cima, A. Gasull, V. Ma˜nosa. Parrondo’s dynamic paradox for the stability of non-hyperbolic fixed points. Discrete Contin. Dyn. Syst. 38 (2018), 889–904. [6] S. Elaydi, R. J. Sacker. Global stability of periodic orbits of non-autonomous difference equations and population biology. J. Differential Equations 208 (2005), 258–273. [7] S. Elaydi, R. J. Sacker. Periodic difference equations, population biology and the Cushing-Henson conjec�tures. Math. Biosci. 201 (2006), 195–207. [8] J. E. Franke, J. F. Selgrade. Attractors for discrete periodic dynamical systems. J. Math. Anal. Appl. 286 (2003), 64–79. [9] G. P. Harmer and D. Abbott. Losing strategies can win by Parrondo’s paradox. Nature (London), Vol. 402, No. 6764 (1999) p. 864. [10] R. Jungers. The Joint Spectral Radius. Spinger, Berlin 2009. [11] J. M. R. Parrondo. How to cheat a bad mathematician. in EEC HC&M Network on Complexity and Chaos (#ERBCHRX-CT940546), ISI, Torino, Italy (1996), Unpublished. [12] J. F. Selgrade, J. H. Roberds. On the structure of attractors for discrete, periodically forced systems with applications to population models. Physica D 158 (2001), 69–82. [13] J. F. Selgrade, J. H. Roberds. Global attractors for a discrete selection model with periodic immigration. J. Difference Equations and Appl. 13 (2007), 275–287.
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