Mariusz Urbański focuses on Mathematical analysis, Pure mathematics, Julia set, Hausdorff dimension and Conformal map. In general Mathematical analysis, his work in Kleinian group, Iterated function system and Spectral gap is often linked to Central limit theorem and Rigidity linking many areas of study. Mariusz Urbański studies Invariant which is a part of Pure mathematics.
Mariusz Urbański has researched Julia set in several fields, including Discrete mathematics and Riemann sphere. His research in Hausdorff dimension intersects with topics in Measure, Invariant measure and Packing dimension. His work is dedicated to discovering how Conformal map, Hausdorff space are connected with Geometry, Filled Julia set and Periodic point and other disciplines.
His main research concerns Pure mathematics, Hausdorff dimension, Mathematical analysis, Discrete mathematics and Conformal map. His work is connected to Meromorphic function, Hausdorff space, Riemann sphere, Rational function and Ergodic theory, as a part of Pure mathematics. His Hausdorff dimension study combines topics from a wide range of disciplines, such as Minkowski–Bouligand dimension and Julia set.
His study in the field of Filled Julia set is also linked to topics like Central limit theorem. His study in Discrete mathematics is interdisciplinary in nature, drawing from both Invariant measure and Invariant. Limit set, Countable set, Limit and Pointwise is closely connected to Iterated function system in his research, which is encompassed under the umbrella topic of Conformal map.
Mariusz Urbański mostly deals with Hausdorff dimension, Pure mathematics, Iterated function system, Discrete mathematics and Meromorphic function. His Hausdorff dimension research incorporates themes from Conjecture, Countable set, Limit set and Julia set. While working in this field, Mariusz Urbański studies both Pure mathematics and Central limit theorem.
His Iterated function system research is multidisciplinary, incorporating elements of Hausdorff measure, Conformal map and Graph. The concepts of his Meromorphic function study are interwoven with issues in Ergodic theory, Transcendental function and Complex plane. His Riemann sphere study is focused on Mathematical analysis in general.
Hausdorff dimension, Pure mathematics, Diophantine approximation, Iterated function system and Discrete mathematics are his primary areas of study. His Hausdorff dimension research is multidisciplinary, relying on both Limit set, Countable set, Measure and Interval. The Hausdorff space, Transfer operator and Invariant measure research Mariusz Urbański does as part of his general Pure mathematics study is frequently linked to other disciplines of science, such as Central limit theorem, therefore creating a link between diverse domains of science.
The study incorporates disciplines such as Fractal and Effective dimension in addition to Hausdorff space. Mariusz Urbański usually deals with Iterated function system and limits it to topics linked to Conformal map and Graph, Markov systems and Carnot cycle. Julia set is a subfield of Mathematical analysis that he explores.
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Dimensions and Measures in Infinite Iterated Function Systems
R. Daniel Mauldin;Mariusz Urbański.
Proceedings of The London Mathematical Society (1996)
Graph Directed Markov Systems: Geometry and Dynamics of Limit Sets
R. Daniel Mauldin;Mariusz Urbanski.
Conformal Fractals: Ergodic Theory Methods
Feliks Przytycki;Mariusz Urbański.
Ergodic theory for Markov fibred systems and parabolic rational maps
Jon Aaronson;Manfred Denker;Mariusz Urbański;Mariusz Urbański.
Transactions of the American Mathematical Society (1993)
Gibbs states on the symbolic space over an infinite alphabet
R. Daniel Mauldin;Mariusz Urbański.
Israel Journal of Mathematics (2001)
On the existence of conformal measures
Manfred Denker;Mariusz Urbański;Mariusz Urbański.
Transactions of the American Mathematical Society (1991)
Conformal iterated function systems with applications to the geometry of continued fractions
R. Mauldin;Mariusz Urbański.
Transactions of the American Mathematical Society (1999)
Ergodic theory of equilibrium states for rational maps
M Denker;M Urbanski.
Thermodynamic Formalism and Multifractal Analysis of Conformal Infinite Iterated Function Systems
Pawel Hanus;R. Daniel Mauldin;Mariusz Urbański.
Acta Mathematica Hungarica (2002)
Harmonic, Gibbs and Hausdorff measures on repellers for holomorphic maps, I
Feliks Przytycki;Mariusz Urbanski;Anna Zdunik.
Annals of Mathematics (1989)
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