152 citations
- AGH University of KrakowPL15 papers
- Jagiellonian UniversityPL9 papers
- Central China Normal UniversityCN7 papers
- Cracow University of TechnologyPL6 papers
- Czech Technical University in PragueCZ6 papers
- Fudan UniversityCN6 papers
- University of HoustonUS6 papers
- Variable Energy Cyclotron CentreIN6 papers
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- Czech Academy of Sciences, Nuclear Physics InstituteCZ5 papers
- Frankfurt Institute for Advanced StudiesDE5 papers
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7 papers · 1 filter
Natural Invariant Measures for Chaotic Game Dynamics: Finding Order in Chaos
Jakub Bielawski, Thiparat Chotibut, Fryderyk Falniowski +2
We study the long-term behavior of the Multiplicative Weights Update (MWU) algorithm in game settings where learning dynamics frequently fail to converge to Nash equilibria and ins…
Kneading the Lorenz attractor
Łukasz Cholewa, Eran Igra
A Lorenz map is a piecewise continuous map, modeled after an idealized version of the Lorenz attractor. In this paper we settle the following question - how much…
On the discrete-time origins of the replicator dynamics: From convergence to instability and chaos
Fryderyk Falniowski, Panayotis Mertikopoulos
We consider three distinct discrete-time models of learning and evolution in games: a biological model based on intra-species selective pressure, the dynamics induced by pairwise p…
Renormalization in Lorenz maps -- completely invariant sets and periodic orbits
Łukasz Cholewa, Piotr Oprocha
The paper deals with dynamics of expanding Lorenz maps, which appear in a natural way as Poincarè maps in geometric models of well-known Lorenz attractor. Using both analytical and…
Transitive dendrite map with zero entropy
Jakub Byszewski, Fryderyk Falniowski, Dominik Kwietniak
Hoehn and Mouron [Ergod. Th. \& Dynam. Sys. (2014) \textbf{34}, 1897--1913] constructed a map on the universal dendrite that is topologically weakly mixing but not mixing. We modif…
Possible generalized entropy convergence rates
Fryderyk Falniowski
We consider an isomorphism invariant for measure-preserving systems - types of generalized entropy convergence rates. We show the connections of this invariant with the types of Sh…