# zbMATH — the first resource for mathematics

Compute Distance To:
 Documents Indexed: 44 Publications since 1961, including 2 Books Biographic References: 2 Publications
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#### Co-Authors

 10 single-authored 8 Kitchens, Bruce P. 7 Tresser, Charles 5 Flatto, Leopold 5 Marcus, Brian H. 4 Weiss, Benjamin 3 Shields, Paul C. 3 Shub, Michael 3 Świrszcz, Grzegorz M. 2 Konheim, Allan G. 2 Martens, Marco 2 McAndrew, M. H. 2 Smorodinsky, Meir 2 Winograd, Shmuel 1 Coppersmith, Don 1 Dedieu, Jean-Pierre 1 Friedman, Joel 1 Goodwyn, L. Wayne 1 Hassner, Martin 1 Keane, Michael S. 1 Margulies, Joseph Y. 1 Micchelli, Charles A. 1 Nowicki, Tomasz 1 Palais, Richard S. 1 Pugh, Charles Chapman 1 Rivlin, Theodore Joseph 1 Worfolk, Patrick A.
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#### Serials

 6 Proceedings of the American Mathematical Society 6 Ergodic Theory and Dynamical Systems 5 Israel Journal of Mathematics 5 Transactions of the American Mathematical Society 2 IEEE Transactions on Information Theory 2 Memoirs of the American Mathematical Society 2 Bulletin of the American Mathematical Society. New Series 1 IMA Journal of Numerical Analysis 1 Journal of Number Theory 1 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 1 Proceedings of the National Academy of Sciences of the United States of America 1 Indagationes Mathematicae. New Series 1 Annals of Numerical Mathematics 1 Discrete and Continuous Dynamical Systems 1 Annals of Mathematical Statistics
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#### Fields

 21 Dynamical systems and ergodic theory (37-XX) 13 Measure and integration (28-XX) 8 General topology (54-XX) 4 Information and communication theory, circuits (94-XX) 3 Differential geometry (53-XX) 2 Combinatorics (05-XX) 2 Topological groups, Lie groups (22-XX) 2 Special functions (33-XX) 2 Convex and discrete geometry (52-XX) 2 Probability theory and stochastic processes (60-XX) 2 Computer science (68-XX) 1 Number theory (11-XX) 1 Group theory and generalizations (20-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 Approximations and expansions (41-XX) 1 Operator theory (47-XX) 1 Biology and other natural sciences (92-XX)

#### Citations contained in zbMATH Open

37 Publications have been cited 1,031 times in 900 Documents Cited by Year
Topological entropy. Zbl 0127.13102
Adler, R. L.; Konheim, Allan G.; McAndrew, M. H.
1965
Newton’s method on Riemannian manifolds and a geometric model for the human spine. Zbl 1056.92002
Adler, Roy L.; Dedieu, Jean-Pierre; Margulies, Joseph Y.; Martens, Marco; Shub, Mike
2002
Similarity of automorphisms of the torus. Zbl 0195.06104
1970
Topological entropy and equivalence of dynamical systems. Zbl 0412.54050
1979
Entropy, a complete metric invariant for automorphisms of the torus. Zbl 0177.08002
1967
Geodesic flows, interval maps, and symbolic dynamics. Zbl 0802.58037
1991
Dynamics of non-ergodic piecewise affine maps of the torus. Zbl 1055.37048
Adler, Roy; Kitchens, Bruce; Tresser, Charles
2001
The ergodic infinite measure preserving transformation of Boole. Zbl 0298.28012
1974
Equivalence of topological Markov shifts. Zbl 0362.54034
Adler, Roy L.; Goodwyn, L. Wayne; Weiss, Benjamin
1977
Algorithms for sliding block codes. An application of symbolic dynamics to information theory. Zbl 0499.94009
Adler, Roy L.; Coppersmith, Don; Hassner, Martin
1983
Symbolic dynamics and Markov partitions. Zbl 0892.58019
1998
Homeomorphic conjugacy of automorphisms on the torus. Zbl 0229.22013
1966
Skew products of Bernoulli shifts with rotations. Zbl 0246.28009
Adler, R. L.; Shields, P. C.
1972
The backward continued fraction map and geodesic flow. Zbl 0563.58019
1984
A construction of a normal number for the continued fraction transformation. Zbl 0448.10050
Adler, Roy; Keane, Michael; Smorodinsky, Meir
1981
Irreducible Markov shifts. Zbl 0244.60053
Adler, R. L.; Shields, P.; Smorodinsky, M.
1972
Cross section maps for geodesic flows. I. (The modular surface). Zbl 0496.58009
1982
Convex dynamics and applications. Zbl 1076.37537
Adler, R. L.; Kitchens, B.; Martens, M.; Pugh, C.; Shub, M.; Tresser, C.
2005
Skew products of Bernoulli shifts with rotations. II. Zbl 0307.28014
Adler, R. L.; Shields, P. C.
1975
Uniform distribution of Kakutani’s interval splitting procedure. Zbl 0362.60014
1977
Ergodic and mixing properties of Chebyshev polynomials. Zbl 0124.06705
Adler, R. L.; Rivlin, T. J.
1964
Cross section map for the geodesic flow on the modular surface. Zbl 0552.58026
1984
$$f$$-expansions revisited. Zbl 0257.28012
1973
Almost topological classification of finite-to-one factor maps between shifts of finite type. Zbl 0606.28015
Adler, Roy; Kitchens, Bruce; Marcus, Brian
1985
Topological conjugacy of linear endomorphisms of the 2-torus. Zbl 0947.37027
Adler, Roy; Tresser, Charles; Worfolk, Patrick A.
1997
Ergodic and mixing properties of infinite memory channels. Zbl 0201.53104
1961
Error diffusion on acute simplices: invariant tiles. Zbl 1377.37026
2017
Finite group actions on shifts of finite type. Zbl 0546.54031
Adler, R. L.; Kitchens, B.; Marcus, B. H.
1985
Convex dynamics with constant input. Zbl 1246.37068
Adler, R. L.; Nowicki, T.; Świrszcz, G.; Tresser, C.
2010
Generalized commuting properties of measure-preserving transformations. Zbl 0178.38502
1965
A note on the entropy of skew product transformations. Zbl 0131.29502
1963
The entropy of Chebyshev polynomials. Zbl 0141.20506
Adler, R. L.; McAndrew, M. H.
1966
Geodesic flows, interval maps, and symbolic dynamics. Zbl 0752.58007
1991
State splitting for variable-length graphs. Zbl 0591.94017
Adler, Roy; Friedman, Joel; Kitchens, Bruce; Marcus, Brian H.
1986
Stably ergodic skew products. Zbl 0989.37019
Adler, Roy; Kitchens, Bruce; Shub, Michael
1996
Invariant and reducing subalgebras of measure preserving transformations. Zbl 0124.32502
1964
A note on translation invariants. Zbl 0111.11105
Adler, R. L.; Konheim, Allan G.
1962
Error diffusion on acute simplices: invariant tiles. Zbl 1377.37026
2017
Convex dynamics with constant input. Zbl 1246.37068
Adler, R. L.; Nowicki, T.; Świrszcz, G.; Tresser, C.
2010
Convex dynamics and applications. Zbl 1076.37537
Adler, R. L.; Kitchens, B.; Martens, M.; Pugh, C.; Shub, M.; Tresser, C.
2005
Newton’s method on Riemannian manifolds and a geometric model for the human spine. Zbl 1056.92002
Adler, Roy L.; Dedieu, Jean-Pierre; Margulies, Joseph Y.; Martens, Marco; Shub, Mike
2002
Dynamics of non-ergodic piecewise affine maps of the torus. Zbl 1055.37048
Adler, Roy; Kitchens, Bruce; Tresser, Charles
2001
Symbolic dynamics and Markov partitions. Zbl 0892.58019
1998
Topological conjugacy of linear endomorphisms of the 2-torus. Zbl 0947.37027
Adler, Roy; Tresser, Charles; Worfolk, Patrick A.
1997
Stably ergodic skew products. Zbl 0989.37019
Adler, Roy; Kitchens, Bruce; Shub, Michael
1996
Geodesic flows, interval maps, and symbolic dynamics. Zbl 0802.58037
1991
Geodesic flows, interval maps, and symbolic dynamics. Zbl 0752.58007
1991
State splitting for variable-length graphs. Zbl 0591.94017
Adler, Roy; Friedman, Joel; Kitchens, Bruce; Marcus, Brian H.
1986
Almost topological classification of finite-to-one factor maps between shifts of finite type. Zbl 0606.28015
Adler, Roy; Kitchens, Bruce; Marcus, Brian
1985
Finite group actions on shifts of finite type. Zbl 0546.54031
Adler, R. L.; Kitchens, B.; Marcus, B. H.
1985
The backward continued fraction map and geodesic flow. Zbl 0563.58019
1984
Cross section map for the geodesic flow on the modular surface. Zbl 0552.58026
1984
Algorithms for sliding block codes. An application of symbolic dynamics to information theory. Zbl 0499.94009
Adler, Roy L.; Coppersmith, Don; Hassner, Martin
1983
Cross section maps for geodesic flows. I. (The modular surface). Zbl 0496.58009
1982
A construction of a normal number for the continued fraction transformation. Zbl 0448.10050
Adler, Roy; Keane, Michael; Smorodinsky, Meir
1981
Topological entropy and equivalence of dynamical systems. Zbl 0412.54050
1979
Equivalence of topological Markov shifts. Zbl 0362.54034
Adler, Roy L.; Goodwyn, L. Wayne; Weiss, Benjamin
1977
Uniform distribution of Kakutani’s interval splitting procedure. Zbl 0362.60014
1977
Skew products of Bernoulli shifts with rotations. II. Zbl 0307.28014
Adler, R. L.; Shields, P. C.
1975
The ergodic infinite measure preserving transformation of Boole. Zbl 0298.28012
1974
$$f$$-expansions revisited. Zbl 0257.28012
1973
Skew products of Bernoulli shifts with rotations. Zbl 0246.28009
Adler, R. L.; Shields, P. C.
1972
Irreducible Markov shifts. Zbl 0244.60053
Adler, R. L.; Shields, P.; Smorodinsky, M.
1972
Similarity of automorphisms of the torus. Zbl 0195.06104
1970
Entropy, a complete metric invariant for automorphisms of the torus. Zbl 0177.08002
1967
Homeomorphic conjugacy of automorphisms on the torus. Zbl 0229.22013
1966
The entropy of Chebyshev polynomials. Zbl 0141.20506
Adler, R. L.; McAndrew, M. H.
1966
Topological entropy. Zbl 0127.13102
Adler, R. L.; Konheim, Allan G.; McAndrew, M. H.
1965
Generalized commuting properties of measure-preserving transformations. Zbl 0178.38502
1965
Ergodic and mixing properties of Chebyshev polynomials. Zbl 0124.06705
Adler, R. L.; Rivlin, T. J.
1964
Invariant and reducing subalgebras of measure preserving transformations. Zbl 0124.32502
1964
A note on the entropy of skew product transformations. Zbl 0131.29502
1963
A note on translation invariants. Zbl 0111.11105
Adler, R. L.; Konheim, Allan G.
1962
Ergodic and mixing properties of infinite memory channels. Zbl 0201.53104
1961
all top 5

#### Cited by 1,017 Authors

 23 Giordano Bruno, Anna 19 Dikranjan, Dikran N. 17 Cánovas, Jose S. 13 Boyle, Mike 12 Adler, Roy Lee 11 Salce, Luigi 10 Absil, Pierre-Antoine 10 Lind, Douglas A. 9 Li, Chong 9 Ma, Dongkui 9 Weiss, Benjamin 8 Ferreira, Orizon Pereira 8 Pollicott, Mark 8 Tresser, Charles 8 Wang, Jinhua 8 Yao, Jen-Chih 7 Block, Louis Stuart 7 Bowen, Rufus 7 Marcus, Brian H. 7 Sharp, Richard W. 7 Tuncel, Selim 7 Virili, Simone 6 Béal, Marie-Pierre 6 Chen, Ercai 6 Fu, Xinchu 6 Huang, Yu 6 Kitchens, Bruce P. 6 Li, Risong 6 Lowenstein, John H. 6 Lu, Tianxiu 5 Alsedà, Lluís 5 Arnoux, Pierre 5 Ito, Shunji 5 Oprocha, Piotr 5 Smorodinsky, Meir 5 Snoha, L’ubomír 5 Trow, Paul B. 5 Vivaldi, Franco 5 Zanardo, Paolo 5 Zhong, Xingfu 4 Aaronson, Jon 4 Aoki, Nobuo 4 Argyros, Ioannis Konstantinos 4 Bai, Zhengjian 4 Balibrea, Francisco 4 Biś, Andrzej 4 Bruin, Henk 4 Castellano, Ilaria 4 Celledoni, Elena 4 Cheng, Wenchiao 4 Cholamjiak, Prasit 4 Du, Bau-Sen 4 Friedman, Joel 4 Gallivan, Kyle A. 4 Goetz, Arek 4 Goldsmith, Brendan 4 Huang, Wen 4 Jiménez López, Víctor 4 Katok, Svetlana R. 4 Krieger, Wolfgang 4 Kupka, Jiří 4 Lima, Yuri 4 Llibre, Jaume 4 López Acedo, Genaro 4 Munoz Guillermo, Maria 4 Pawlak, Ryszard Jerzy 4 Perrin, Dominique 4 Petersen, Karl E. 4 Schmidt, Klaus 4 Shields, Paul C. 4 Ugarcovici, Ilie 4 Vetokhin, A. N. 4 Wang, Xiangmei 4 Wang, Yupan 4 Wu, Xinxing 4 Xu, Leiye 4 Yan, Kesong 4 Yao, Tengteng 4 Zeng, Fanping 4 Zhao, Zhi 4 Zhu, Changrong 3 Amigó, José María 3 Anglès d’Auriac, Jean-Christian 3 Ashley, Jonathan J. 3 Ashwin, Peter 3 Boukraa, Salah 3 Boyarsky, Abraham 3 Burton, Robert M. jun. 3 Cánovas Peña, Jose Salvador 3 Colonius, Fritz 3 Das, Ruchi 3 Das, Tarun Kumar 3 Einsiedler, Manfred Leopold 3 Fried, David 3 García Guirao, Juan Luis 3 Goodwyn, L. Wayne 3 Haas, Andrew 3 Hochman, Michael 3 Huang, Xiaojun 3 Hüper, Knut ...and 917 more Authors
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#### Cited in 234 Serials

 52 Transactions of the American Mathematical Society 51 Ergodic Theory and Dynamical Systems 44 Israel Journal of Mathematics 39 Proceedings of the American Mathematical Society 34 Topology and its Applications 22 Journal of Mathematical Analysis and Applications 20 Chaos 19 Discrete and Continuous Dynamical Systems 18 Mathematical Systems Theory 17 Chaos, Solitons and Fractals 16 Dynamical Systems 14 Monatshefte für Mathematik 12 Inventiones Mathematicae 12 Theoretical Computer Science 11 Communications in Mathematical Physics 11 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 10 Bulletin of the Australian Mathematical Society 9 Physica D 9 Bulletin of the American Mathematical Society. New Series 9 SIAM Journal on Optimization 8 Journal of Statistical Physics 8 Journal of Computational and Applied Mathematics 8 Journal of Differential Equations 8 Journal of Number Theory 8 Journal of Optimization Theory and Applications 8 Journal of Global Optimization 8 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 7 Indagationes Mathematicae. New Series 7 Journal of Mathematical Chemistry 6 Mathematical Notes 6 Nonlinearity 6 Applied Mathematics and Computation 6 Geometriae Dedicata 6 Linear Algebra and its Applications 6 Journal of Dynamics and Differential Equations 6 Discrete and Continuous Dynamical Systems. Series B 5 Functional Analysis and its Applications 5 Journal of Functional Analysis 5 Advances in Applied Mathematics 5 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section B. Calcul des Probabilités et Statistique 5 Journal of Difference Equations and Applications 5 Qualitative Theory of Dynamical Systems 5 Bulletin of the American Mathematical Society 5 Proceedings of the Japan Academy 5 Journal of Modern Dynamics 5 Topological Algebra and its Applications 4 Journal d’Analyse Mathématique 4 Advances in Mathematics 4 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 4 Journal of Algebra 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 4 Journal de Théorie des Nombres de Bordeaux 4 Differential Equations 4 Asian-European Journal of Mathematics 3 Journal of the Franklin Institute 3 Journal of Mathematical Physics 3 The Mathematical Intelligencer 3 Annales de l’Institut Fourier 3 Bulletin de la Société Mathématique de France 3 Duke Mathematical Journal 3 Fuzzy Sets and Systems 3 Publications of the Research Institute for Mathematical Sciences, Kyoto University 3 Acta Applicandae Mathematicae 3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 SIAM Journal on Matrix Analysis and Applications 3 Geometric and Functional Analysis. GAFA 3 Mathematical Programming. Series A. Series B 3 Computational Optimization and Applications 3 Journal of the European Mathematical Society (JEMS) 3 Acta Mathematica Sinica. English Series 3 Communications in Nonlinear Science and Numerical Simulation 3 Kodai Mathematical Seminar Reports 3 Science China. Mathematics 2 Rocky Mountain Journal of Mathematics 2 Ukrainian Mathematical Journal 2 Mathematics of Computation 2 Automatica 2 Journal of Economic Theory 2 Journal of the Korean Mathematical Society 2 Journal of Pure and Applied Algebra 2 Journal of Soviet Mathematics 2 Kybernetika 2 Mathematica Slovaca 2 Mathematische Zeitschrift 2 Numerische Mathematik 2 Semigroup Forum 2 SIAM Journal on Control and Optimization 2 Tokyo Journal of Mathematics 2 Systems & Control Letters 2 Optimization 2 Probability Theory and Related Fields 2 Journal of Complexity 2 Journal of Theoretical Probability 2 Applied Mathematics Letters 2 Journal of the American Mathematical Society 2 Forum Mathematicum 2 Japan Journal of Industrial and Applied Mathematics 2 Numerical Algorithms 2 Boletim da Sociedade Brasileira de Matemática. Nova Série 2 Journal of Nonlinear Science ...and 134 more Serials
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#### Cited in 53 Fields

 560 Dynamical systems and ergodic theory (37-XX) 180 Measure and integration (28-XX) 160 General topology (54-XX) 68 Number theory (11-XX) 58 Numerical analysis (65-XX) 54 Probability theory and stochastic processes (60-XX) 45 Operations research, mathematical programming (90-XX) 44 Group theory and generalizations (20-XX) 40 Computer science (68-XX) 37 Topological groups, Lie groups (22-XX) 37 Information and communication theory, circuits (94-XX) 33 Combinatorics (05-XX) 30 Operator theory (47-XX) 28 Differential geometry (53-XX) 23 Linear and multilinear algebra; matrix theory (15-XX) 23 Functions of a complex variable (30-XX) 22 Calculus of variations and optimal control; optimization (49-XX) 20 Global analysis, analysis on manifolds (58-XX) 19 Real functions (26-XX) 18 Manifolds and cell complexes (57-XX) 17 Systems theory; control (93-XX) 15 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 12 Convex and discrete geometry (52-XX) 11 Ordinary differential equations (34-XX) 11 Functional analysis (46-XX) 11 Statistical mechanics, structure of matter (82-XX) 10 Commutative algebra (13-XX) 10 Biology and other natural sciences (92-XX) 9 Associative rings and algebras (16-XX) 8 Mechanics of particles and systems (70-XX) 7 Mathematical logic and foundations (03-XX) 7 Algebraic geometry (14-XX) 7 Difference and functional equations (39-XX) 6 Category theory; homological algebra (18-XX) 6 Statistics (62-XX) 6 Quantum theory (81-XX) 5 Abstract harmonic analysis (43-XX) 4 Several complex variables and analytic spaces (32-XX) 3 Partial differential equations (35-XX) 3 Algebraic topology (55-XX) 3 Fluid mechanics (76-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 $$K$$-theory (19-XX) 2 Special functions (33-XX) 2 Approximations and expansions (41-XX) 2 Geometry (51-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Field theory and polynomials (12-XX) 1 Sequences, series, summability (40-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Mechanics of deformable solids (74-XX) 1 Relativity and gravitational theory (83-XX)

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