21 citations · 52 across the 13 of their papers we have counts for
10 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…
Strange bifurcation diagrams
Jakub Bielawski, Thiparat Chotibut, Fryderyk Falniowski +2
We investigate a family of one dimensional maps for which the bifurcation diagram looks differently than the usual ones. We describe and exemplify various unique and interesting ph…
The emergence of chaos in population game dynamics induced by comparisons
Jakub Bielawski, Łukasz Cholewa, Fryderyk Falniowski
Precise description of population game dynamics introduced by revision protocols - an economic model describing the agent's propensity to switch to a better-performing strategy - i…
Interval maps mimicking circle rotations
Jakub Bielawski, Thiparat Chotibut, Fryderyk Falniowski +2
We investigate the dynamics of maps of the real line whose behavior on an invariant interval is close to a rational rotation on the circle. We concentrate on a specific two-paramet…
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…
Family of chaotic maps from game theory
Thiparat Chotibut, Fryderyk Falniowski, Michal Misiurewicz +1
From a two-agent, two-strategy congestion game where both agents apply the multiplicative weights update algorithm, we obtain a two-parameter family of maps of the unit square to i…
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…
Two results on entropy, chaos, and independence in symbolic dynamics
Fryderyk Falniowski, Marcin Kulczycki, Dominik Kwietniak +1
We survey the connections between entropy, chaos, and independence in topological dynamics. We present extensions of two classical results placing the following notions in the cont…
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…
On the connections of the generalized entropies and Kolmogorov-Sinai entropies
Fryderyk Falniowski
We consider the concept of generalized measure-theoretic entropy, where instead of the Shannon entropy function we consider an arbitrary concave function defined on the unit interv…