1.4k citations · 11.5k across the 204 of their papers we have counts for
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On the entropy devil's staircase in a family of gap-tent maps
Karol Zyczkowski, Erik M. Bollt
We analyze dynamical properties of a "gap-tent map" - a family of 1D maps with a symmetric gap, which mimics the presence of noise in physical realizations of chaotic systems. We d…
Quantum baker map on the sphere
Prot Pakonski, Andrzej Ostruszka, Karol Zyczkowski
We define a class of dynamical systems on the sphere analogous to the baker map on the torus. The classical maps are characterized by dynamical entropy equal to ln 2. We construct…
On the volume of the set of mixed entangled states
Karol Zyczkowski, Pawel Horodecki, Anna Sanpera +1
A natural measure in the space of density matrices describing N-dimensional quantum systems is proposed. We study the probability P that a quantum state chosen randomly with respec…
Entropy computing via integration over fractal measures
Wojciech Slomczynski, Jaroslaw Kwapien, Karol Zyczkowski
We discuss the properties of invariant measures corresponding to iterated function systems (IFSs) with place-dependent probabilities and compute their Renyi entropies, generalized…
Risk-return arguments applied to options with trading costs
Erik Aurell, Karol Życzkowski
We study the problem of option pricing and hedging strategies within the frame-work of risk-return arguments. An economic agent is described by a utility function that depends on p…
Quantum scattering in the strip: from ballistic to localized regimes
Robert Gebarowski, Petr Seba, Karol Zyczkowski +1
Quantum scattering is studied in a system consisting of randomly distributed point scatterers in the strip. The model is continuous yet exactly solvable. Varying the number of scat…