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Author ID: arnoux.pierre Recent zbMATH articles by "Arnoux, Pierre"
Published as: Arnoux, Pierre; Arnoux, P.
Homepage: http://iml.univ-mrs.fr/~arnoux/
External Links: MGP · dblp · IdRef · theses.fr
Member of Collective: Fogg, N. Pytheas

Publications by Year

Citations contained in zbMATH Open

39 Publications have been cited 704 times in 478 Documents Cited by Year
Geometric representation of sequences of complexity \(2n+1\). (Représentation géométrique de suites de complexité \(2n+1\).) Zbl 0789.28011
Arnoux, Pierre; Rauzy, Gérard
144
1991
Pisot substitutions and Rauzy fractals. Zbl 1007.37001
Arnoux, Pierre; Ito, Shunji
104
2001
Construction de difféomorphismes pseudo-Anosov. Zbl 0478.58023
Arnoux, Pierre; Yoccoz, Jean-Christophe
49
1981
Higher dimensional extensions of substitutions and their dual maps. Zbl 0987.11013
Sano, Yuki; Arnoux, Pierre; Ito, Shunji
32
2001
Complexity of sequences defined by billiard in the cube. Zbl 0791.58034
Arnoux, Pierre; Mauduit, Christian; Shiokawa, Iekata; Tamura, Jun-Ichi
29
1994
Sur l’unique ergodicité des 1-formes fermées singulières. (Unique ergodicity of closed singular 1-forms). Zbl 0577.58021
Arnoux, Pierre; Levitt, Gilbert
28
1986
Un exemple de semi-conjugaison entre un échange d’intervalles et une translation sur le tore. (An example of semi-conjugacy between an interval exchange and a translation on the torus.). Zbl 0703.58045
Arnoux, Pierre
24
1988
Discrete planes, \({\mathbb Z}^2\)-actions, Jacobi-Perron algorithm and substitutions. Zbl 1017.11006
Arnoux, Pierre; Berthé, Valérie; Ito, Shunji
23
2002
Cutting and stacking, interval exchanges and geometric models. Zbl 0558.58019
Arnoux, Pierre; Ornstein, Donald S.; Weiss, Benjamin
23
1985
Gauss measures for multidimensional continued fraction algorithms. (Mesures de Gauss pour des algorithmes de fractions continues multidimensionnelles.) Zbl 0801.11036
Arnoux, Pierre; Nogueira, Arnaldo
19
1993
Anosov families, renormalization and non-stationary subshifts. Zbl 1140.37314
Arnoux, Pierre; Fisher, Albert M.
16
2005
Tilings, quasicrystals, discrete planes, generalized substitutions, and multidimensional continued fractions. Zbl 1017.68147
Arnoux, Pierre; Berthé, Valérie; Ei, Hiromi; Ito, Shunji
15
2001
Echanges d’intervalles et flots sur les surfaces. Zbl 0471.28014
Arnoux, Pierre
15
1981
Two-dimensional iterated morphisms and discrete planes. Zbl 1068.37004
Arnoux, Pierre; Berthé, Valérie; Siegel, Anne
12
2004
Functional stepped surfaces, flips, and generalized substitutions. Zbl 1119.68136
Arnoux, Pierre; Berthé, Valérie; Fernique, Thomas; Jamet, Damien
12
2007
The Rauzy gasket. Zbl 1268.28007
Arnoux, Pierre; Starosta, Štěpán
12
2013
The Kühnel triangulation of the complex projective plane from the view point of complex crystallography. II. Zbl 0753.52002
Arnoux, Pierre; Marin, Alexis
11
1991
On some symmetric multidimensional continued fraction algorithms. Zbl 1403.37089
Arnoux, Pierre; Labbé, Sébastien
11
2016
The coding for geodesic flows on a modular surface. (Le codage du flot géodésique sur la surface modulaire.) Zbl 0812.58065
Arnoux, Pierre
11
1994
Algebraic numbers, free group automorphisms and substitutions on the plane. Zbl 1254.37015
Arnoux, Pierre; Furukado, Maki; Harriss, Edmund; Ito, Shunji
11
2011
Veech surfaces with nonperiodic directions in the trace field. Zbl 1186.37050
Arnoux, Pierre; Schmidt, Thomas A.
11
2009
The scenery flow for geometric structures on the torus: The linear setting. Zbl 0993.37018
Arnoux, P.; Fisher, A. M.
10
2001
Continued fractions on the Veech surfaces. (Fractions continues sur les surfaces de Veech.) Zbl 1029.11035
Arnoux, Pierre; Hubert, Pascal
10
2000
Fractal representation of the attractive lamination of an automorphism of the free group. Zbl 1146.20020
Arnoux, Pierre; Berthé, Valérie; Hilion, Arnaud; Siegel, Anne
10
2006
Geometrical models for substitutions. Zbl 1266.37008
Arnoux, Pierre; Bernat, Julien; Bressaud, Xavier
10
2011
Trajectories of rotations. Zbl 0921.11033
Arnoux, Pierre; Ferenczi, Sébastien; Hubert, Pascal
10
1999
Cross sections for geodesic flows and \(\alpha\)-continued fractions. Zbl 1268.37038
Arnoux, Pierre; Schmidt, Thomas A.
9
2013
Some remarks about Fibonacci multiplication. Zbl 0711.11008
Arnoux, Pierre
6
1989
Sturm numbers and substitution invariance of 3iet words. Zbl 1202.11021
Arnoux, Pierre; Berthé, Valérie; Masáková, Zuzana; Pelantová, Edita
5
2008
Rauzy’s conjecture on billiards in the cube. Zbl 0814.11014
Arnoux, Pierre; Mauduit, Christian; Shiokawa, Iekata; Tamura, Jun-ichi
4
1994
Random product of substitutions with the same incidence matrix. Zbl 1418.37021
Arnoux, Pierre; Mizutani, Masahiro; Sellami, Tarek
3
2014
Recoding Sturmian sequences on a subshift of finite type chaos from order: a worked out example. Zbl 1333.37006
Arnoux, Pierre
3
2001
Ergodicité générique des billards polygonaux [d’après Kerckhoff, Masur, Smillie]. (Generic ergodicity of polygonal billiards). Zbl 0671.58023
Arnoux, Pierre
3
1988
What is …a Rauzy fractal? Zbl 1338.28001
Arnoux, Pierre; Harriss, Edmund
2
2014
Commensurable continued fractions. Zbl 1351.37164
Arnoux, Pierre; Schmidt, Thomas A.
2
2014
Un exemple de difféomorphisme pseudo-Anosov. (An example of pseudo- Anosov diffeomorphism). Zbl 0722.57015
Arnoux, Pierre; Fathi, Albert
2
1991
Complexity of sequences generated by unipotent recurrences. (Complexité de suites engendrées par des récurrences unipotentes.) Zbl 0860.68082
Arnoux, Pierre; Mauduit, Christian
1
1996
Continued fractions: natural extensions and invariant measures. Zbl 1372.37019
Arnoux, Pierre
1
2016
Substitution and tiling dynamics: introduction to self-inducing structures. Lecture notes from the research school on tiling dynamical systems, CIRM Jean-Morlet Chair, Marseille, France, Fall 2017. Zbl 1454.37001
1
2020
Substitution and tiling dynamics: introduction to self-inducing structures. Lecture notes from the research school on tiling dynamical systems, CIRM Jean-Morlet Chair, Marseille, France, Fall 2017. Zbl 1454.37001
1
2020
On some symmetric multidimensional continued fraction algorithms. Zbl 1403.37089
Arnoux, Pierre; Labbé, Sébastien
11
2016
Continued fractions: natural extensions and invariant measures. Zbl 1372.37019
Arnoux, Pierre
1
2016
Random product of substitutions with the same incidence matrix. Zbl 1418.37021
Arnoux, Pierre; Mizutani, Masahiro; Sellami, Tarek
3
2014
What is …a Rauzy fractal? Zbl 1338.28001
Arnoux, Pierre; Harriss, Edmund
2
2014
Commensurable continued fractions. Zbl 1351.37164
Arnoux, Pierre; Schmidt, Thomas A.
2
2014
The Rauzy gasket. Zbl 1268.28007
Arnoux, Pierre; Starosta, Štěpán
12
2013
Cross sections for geodesic flows and \(\alpha\)-continued fractions. Zbl 1268.37038
Arnoux, Pierre; Schmidt, Thomas A.
9
2013
Algebraic numbers, free group automorphisms and substitutions on the plane. Zbl 1254.37015
Arnoux, Pierre; Furukado, Maki; Harriss, Edmund; Ito, Shunji
11
2011
Geometrical models for substitutions. Zbl 1266.37008
Arnoux, Pierre; Bernat, Julien; Bressaud, Xavier
10
2011
Veech surfaces with nonperiodic directions in the trace field. Zbl 1186.37050
Arnoux, Pierre; Schmidt, Thomas A.
11
2009
Sturm numbers and substitution invariance of 3iet words. Zbl 1202.11021
Arnoux, Pierre; Berthé, Valérie; Masáková, Zuzana; Pelantová, Edita
5
2008
Functional stepped surfaces, flips, and generalized substitutions. Zbl 1119.68136
Arnoux, Pierre; Berthé, Valérie; Fernique, Thomas; Jamet, Damien
12
2007
Fractal representation of the attractive lamination of an automorphism of the free group. Zbl 1146.20020
Arnoux, Pierre; Berthé, Valérie; Hilion, Arnaud; Siegel, Anne
10
2006
Anosov families, renormalization and non-stationary subshifts. Zbl 1140.37314
Arnoux, Pierre; Fisher, Albert M.
16
2005
Two-dimensional iterated morphisms and discrete planes. Zbl 1068.37004
Arnoux, Pierre; Berthé, Valérie; Siegel, Anne
12
2004
Discrete planes, \({\mathbb Z}^2\)-actions, Jacobi-Perron algorithm and substitutions. Zbl 1017.11006
Arnoux, Pierre; Berthé, Valérie; Ito, Shunji
23
2002
Pisot substitutions and Rauzy fractals. Zbl 1007.37001
Arnoux, Pierre; Ito, Shunji
104
2001
Higher dimensional extensions of substitutions and their dual maps. Zbl 0987.11013
Sano, Yuki; Arnoux, Pierre; Ito, Shunji
32
2001
Tilings, quasicrystals, discrete planes, generalized substitutions, and multidimensional continued fractions. Zbl 1017.68147
Arnoux, Pierre; Berthé, Valérie; Ei, Hiromi; Ito, Shunji
15
2001
The scenery flow for geometric structures on the torus: The linear setting. Zbl 0993.37018
Arnoux, P.; Fisher, A. M.
10
2001
Recoding Sturmian sequences on a subshift of finite type chaos from order: a worked out example. Zbl 1333.37006
Arnoux, Pierre
3
2001
Continued fractions on the Veech surfaces. (Fractions continues sur les surfaces de Veech.) Zbl 1029.11035
Arnoux, Pierre; Hubert, Pascal
10
2000
Trajectories of rotations. Zbl 0921.11033
Arnoux, Pierre; Ferenczi, Sébastien; Hubert, Pascal
10
1999
Complexity of sequences generated by unipotent recurrences. (Complexité de suites engendrées par des récurrences unipotentes.) Zbl 0860.68082
Arnoux, Pierre; Mauduit, Christian
1
1996
Complexity of sequences defined by billiard in the cube. Zbl 0791.58034
Arnoux, Pierre; Mauduit, Christian; Shiokawa, Iekata; Tamura, Jun-Ichi
29
1994
The coding for geodesic flows on a modular surface. (Le codage du flot géodésique sur la surface modulaire.) Zbl 0812.58065
Arnoux, Pierre
11
1994
Rauzy’s conjecture on billiards in the cube. Zbl 0814.11014
Arnoux, Pierre; Mauduit, Christian; Shiokawa, Iekata; Tamura, Jun-ichi
4
1994
Gauss measures for multidimensional continued fraction algorithms. (Mesures de Gauss pour des algorithmes de fractions continues multidimensionnelles.) Zbl 0801.11036
Arnoux, Pierre; Nogueira, Arnaldo
19
1993
Geometric representation of sequences of complexity \(2n+1\). (Représentation géométrique de suites de complexité \(2n+1\).) Zbl 0789.28011
Arnoux, Pierre; Rauzy, Gérard
144
1991
The Kühnel triangulation of the complex projective plane from the view point of complex crystallography. II. Zbl 0753.52002
Arnoux, Pierre; Marin, Alexis
11
1991
Un exemple de difféomorphisme pseudo-Anosov. (An example of pseudo- Anosov diffeomorphism). Zbl 0722.57015
Arnoux, Pierre; Fathi, Albert
2
1991
Some remarks about Fibonacci multiplication. Zbl 0711.11008
Arnoux, Pierre
6
1989
Un exemple de semi-conjugaison entre un échange d’intervalles et une translation sur le tore. (An example of semi-conjugacy between an interval exchange and a translation on the torus.). Zbl 0703.58045
Arnoux, Pierre
24
1988
Ergodicité générique des billards polygonaux [d’après Kerckhoff, Masur, Smillie]. (Generic ergodicity of polygonal billiards). Zbl 0671.58023
Arnoux, Pierre
3
1988
Sur l’unique ergodicité des 1-formes fermées singulières. (Unique ergodicity of closed singular 1-forms). Zbl 0577.58021
Arnoux, Pierre; Levitt, Gilbert
28
1986
Cutting and stacking, interval exchanges and geometric models. Zbl 0558.58019
Arnoux, Pierre; Ornstein, Donald S.; Weiss, Benjamin
23
1985
Construction de difféomorphismes pseudo-Anosov. Zbl 0478.58023
Arnoux, Pierre; Yoccoz, Jean-Christophe
49
1981
Echanges d’intervalles et flots sur les surfaces. Zbl 0471.28014
Arnoux, Pierre
15
1981
all top 5

Cited by 420 Authors

32 Berthé, Valérie
18 Hubert, Pascal
16 Ferenczi, Sébastien
15 Arnoux, Pierre
13 Pelantová, Edita
13 Zamboni, Luca Quardo
12 Gelbukh, Irina
12 Sirvent, Víctor F.
11 Schmidt, Thomas A.
11 Thuswaldner, Jörg Maximilian
10 Ito, Shunji
9 Masáková, Zuzana
8 Akiyama, Shigeki
8 Fernique, Thomas
8 Justin, Jacques
8 Tan, Bo
8 Vuillon, Laurent
7 Cassaigne, Julien
7 Glen, Amy
7 Rao, Hui
7 Richomme, Gwénaël
7 Siegel, Anne
7 Steiner, Wolfgang
7 Tijdeman, Robert
6 Leroy, Julien
6 Messaoudi, Ali
6 Reutenauer, Christophe
6 Wen, Zhixiong
5 Bédaride, Nicolas
5 de Luca, Aldo
5 De Luca, Alessandro
5 Lanneau, Erwan
5 Levitt, Gilbert
5 Loridant, Benoit
5 Perrin, Dominique
5 Pirillo, Giuseppe
5 Sellami, Tarek
5 Starosta, Štěpán
5 Surer, Paul
5 Wen, Zhi-Ying
5 Zhang, Yiping
4 Ambrož, Petr
4 Bucci, Michelangelo
4 Chekhova, Nataliya
4 Datta, Basudeb
4 De Felice, Clelia
4 Dolce, Francesco
4 Durand, Fabien
4 Fisher, Albert Meads
4 Labbé, Sébastien
4 Lopez, Luis-Miguel
4 Narbel, Philippe
4 Restivo, Antonio
4 Robinson, E. Arthur jun.
4 Shutov, Anton V.
4 Tamura, Jun-ichi
3 Adamczewski, Boris
3 Allouche, Jean-Paul Simon
3 Bagchi, Bhaskar
3 Balková, L’ubomíra
3 Barge, Marcy M.
3 Bernat, Julien
3 Blanchet-Sadri, Francine
3 Calta, Kariane
3 Didier, Gilles
3 Ei, Hiromi
3 Furukado, Maki
3 Gaboriau, Damien
3 Jolivet, Timo
3 Mauduit, Christian
3 McMullen, Curtis Tracy
3 Merriman, Claire
3 Minervino, Milton
3 Muentes Acevedo, Jeovanny de Jesus
3 Nogueira, Arnaldo C. R.
3 Paquin, Geneviève
3 Priebe Frank, Natalie
3 Rigo, Michel
3 Rindone, Giuseppina
3 Yang, Yamin
2 Ammar, Hamdi
2 Aranson, Samuil Khaĭmovich
2 Araújo, Isabel M.
2 Avila Cordeiro de Melo, Artur
2 Berstel, Jean
2 Bertazzon, Jean-Francois
2 Blume, Frank
2 Boca, Florin-Petre
2 Bodini, Olivier
2 Borel, Jean-Pierre
2 Boshernitzan, Michael D.
2 Bressaud, Xavier
2 Brimkov, Valentin E.
2 Bruyère, Véronique
2 Bufetov, Aleksandr Igorevich
2 Bugeaud, Yann
2 Charlier, Emilie
2 Cobo, Milton
2 Damanik, David
2 Delecroix, Vincent
...and 320 more Authors
all top 5

Cited in 135 Serials

67 Theoretical Computer Science
25 Annales de l’Institut Fourier
22 Ergodic Theory and Dynamical Systems
14 RAIRO. Theoretical Informatics and Applications
13 Journal de Théorie des Nombres de Bordeaux
12 Journal d’Analyse Mathématique
12 European Journal of Combinatorics
10 Transactions of the American Mathematical Society
10 Discrete and Continuous Dynamical Systems
10 Comptes Rendus. Mathématique. Académie des Sciences, Paris
9 Geometriae Dedicata
9 Advances in Applied Mathematics
8 Topology and its Applications
7 Discrete Mathematics
7 Israel Journal of Mathematics
7 Proceedings of the American Mathematical Society
6 Discrete Applied Mathematics
6 Advances in Mathematics
6 Bulletin de la Société Mathématique de France
6 Inventiones Mathematicae
6 Journal of Number Theory
6 Monatshefte für Mathematik
6 Discrete & Computational Geometry
6 Indagationes Mathematicae. New Series
6 Dynamical Systems
6 Journal of Modern Dynamics
5 Journal of Mathematical Analysis and Applications
5 Nonlinearity
4 Mathematical Notes
4 Mathematische Annalen
4 Experimental Mathematics
3 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
3 Czechoslovak Mathematical Journal
3 Duke Mathematical Journal
3 Mathematische Zeitschrift
3 Osaka Journal of Mathematics
3 International Journal of Foundations of Computer Science
3 Bulletin of the American Mathematical Society. New Series
3 Proceedings of the Steklov Institute of Mathematics
3 RAIRO. Theoretical Informatics and Applications
2 Communications in Mathematical Physics
2 Journal of Geometry and Physics
2 Acta Arithmetica
2 Journal of Pure and Applied Algebra
2 Mathematica Slovaca
2 Nagoya Mathematical Journal
2 Quaestiones Mathematicae
2 Tokyo Journal of Mathematics
2 Information and Computation
2 Applied Mathematics Letters
2 Journal of the American Mathematical Society
2 Differential Geometry and its Applications
2 Geometric and Functional Analysis. GAFA
2 Journal of Mathematical Sciences (New York)
2 Annals of Mathematics. Second Series
2 Qualitative Theory of Dynamical Systems
2 Stochastics and Dynamics
2 International Journal of Number Theory
2 Chebyshevskiĭ Sbornik
2 Groups, Geometry, and Dynamics
2 Actes des Rencontres du C.I.R.M.
1 American Mathematical Monthly
1 Bulletin of the Australian Mathematical Society
1 Computers & Mathematics with Applications
1 Journal of Statistical Physics
1 Letters in Mathematical Physics
1 Rocky Mountain Journal of Mathematics
1 Mathematics of Computation
1 Reviews in Mathematical Physics
1 Chaos, Solitons and Fractals
1 The Mathematical Intelligencer
1 Canadian Journal of Mathematics
1 Functiones et Approximatio. Commentarii Mathematici
1 Journal of Algebra
1 Journal of Combinatorial Theory. Series A
1 Journal of Computer and System Sciences
1 Journal of Functional Analysis
1 Journal of the Korean Mathematical Society
1 Journal of the Mathematical Society of Japan
1 Journal of Soviet Mathematics
1 Memoirs of the American Mathematical Society
1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
1 Proceedings of the London Mathematical Society. Third Series
1 Semigroup Forum
1 Siberian Mathematical Journal
1 Tohoku Mathematical Journal. Second Series
1 Transactions of the Moscow Mathematical Society
1 Combinatorica
1 Chinese Annals of Mathematics. Series B
1 Acta Mathematica Hungarica
1 Journal of Symbolic Computation
1 Asia-Pacific Journal of Operational Research
1 International Journal of Algebra and Computation
1 Discrete Event Dynamic Systems
1 Journal de Mathématiques Pures et Appliquées. Neuvième Série
1 Pattern Recognition
1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
1 Expositiones Mathematicae
1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
...and 35 more Serials
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Cited in 38 Fields

249 Dynamical systems and ergodic theory (37-XX)
173 Computer science (68-XX)
138 Number theory (11-XX)
67 Measure and integration (28-XX)
56 Convex and discrete geometry (52-XX)
54 Manifolds and cell complexes (57-XX)
39 Combinatorics (05-XX)
33 Group theory and generalizations (20-XX)
22 Functions of a complex variable (30-XX)
19 Global analysis, analysis on manifolds (58-XX)
10 Several complex variables and analytic spaces (32-XX)
10 Differential geometry (53-XX)
10 General topology (54-XX)
9 Probability theory and stochastic processes (60-XX)
5 Operator theory (47-XX)
5 Algebraic topology (55-XX)
4 General and overarching topics; collections (00-XX)
4 Mathematical logic and foundations (03-XX)
4 General algebraic systems (08-XX)
4 Linear and multilinear algebra; matrix theory (15-XX)
4 Geometry (51-XX)
3 Algebraic geometry (14-XX)
3 Topological groups, Lie groups (22-XX)
3 Statistics (62-XX)
3 Statistical mechanics, structure of matter (82-XX)
3 Information and communication theory, circuits (94-XX)
2 History and biography (01-XX)
2 Field theory and polynomials (12-XX)
2 Partial differential equations (35-XX)
2 Difference and functional equations (39-XX)
2 Numerical analysis (65-XX)
2 Operations research, mathematical programming (90-XX)
1 Special functions (33-XX)
1 Sequences, series, summability (40-XX)
1 Harmonic analysis on Euclidean spaces (42-XX)
1 Integral equations (45-XX)
1 Quantum theory (81-XX)
1 Relativity and gravitational theory (83-XX)

Citations by Year