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On quantum iterated function systems [PDF]
Open Physics, 2004 Quantum Iterated Function System on a complex projective space is defined by a family of linear operators on a complex Hilbert space. The operators define both the maps and their probabilities by one algebraic formula.
Jadczyk Arkadiusz
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Quantum Iterated Function Systems [PDF]
Physical Review E, 2003 Iterated functions system (IFS) is defined by specifying a set of functions in a classical phase space, which act randomly on an initial point. In an analogous way, we define a quantum iterated functions system (QIFS), where functions act randomly with ...
A. Lasota +48 more
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Entropy of Iterated Function Systems and Their Relations with Black Holes and Bohr-Like Black Holes Entropies [PDF]
Entropy, 2018 In this paper we consider the metric entropies of the maps of an iterated function system deduced from a black hole which are known the Bekenstein–Hawking entropies and its subleading corrections.
Christian Corda +3 more
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Quantitative recurrence and the shrinking target problem for overlapping iterated function systems [PDF]
Advances in Mathematics, 2023 In this paper we study quantitative recurrence and the shrinking target problem for dynamical systems coming from overlapping iterated function systems.
S. Baker, Henna Koivusalo
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Iterated Function Systems: A Comprehensive Survey [PDF]
arXiv.org, 2022 We provide an overview of iterated function systems (IFS), where randomly chosen state-to-state maps are applied iteratively to a state. We aim to summarize the state of art and, where possible, identify fundamental challenges and opportunities for ...
Ramen Ghosh, Jakub Marecek
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Intrinsic Diophantine approximation for overlapping iterated function systems [PDF]
Mathematische Annalen, 2021 In this paper we study a family of limsup sets that are defined using iterated function systems. Our main result is an analogue of Khintchine’s theorem for these sets.
S. Baker
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Iterated Random Functions [PDF]
SIAM Review, 1999 Summary: Iterated random functions are used to draw pictures or simulate large Ising models, among other applications. They offer a method for studying the steady state distribution of a Markov chain, and give useful bounds on rates of convergence in a variety of examples. The present paper surveys the field and presents some new examples.
Diaconis, Persi, Freedman, David
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Thermodynamic formalism for invariant measures in iterated function systems with overlaps [PDF]
, 2021 We study images of equilibrium (Gibbs) states for a class of non-invertible transformations associated to conformal iterated function systems with overlaps S.
E. Mihailescu
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Fractal and Fractional, 2021 In 2021, Mork and Ulness studied the Mandelbrot and Julia sets for a generalization of the well-explored function ηλ(z)=z2+λ. Their generalization was based on the composition of ηλ with the Möbius transformation μ(z)=1z at each iteration step ...
Pavel Trojovský, K Venkatachalam
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Dimension estimates for $C^1$ iterated function systems and repellers. Part I
Ergodic Theory and Dynamical Systems, 2022 This is the first paper in a two-part series containing some results on dimension estimates for $C^1$ iterated function systems and repellers. In this part, we prove that the upper box-counting dimension of the attractor of any $C^1$ iterated ...
De-Jun Feng, K. Simon
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