# zbMATH — the first resource for mathematics

## Walters, Peter

Compute Distance To:
 Author ID: walters.peter Published as: Walters, P.; Walters, Peter
 Documents Indexed: 45 Publications since 1967, including 5 Books Biographic References: 1 Publication

#### Co-Authors

 36 single-authored 3 Parry, William 1 Bowen, Rufus 1 Ledrappier, François 1 Palmer, Marion Rachel 1 Schmidt, Klaus
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#### Serials

 8 Transactions of the American Mathematical Society 3 Journal of the London Mathematical Society. Second Series 3 Mathematical Systems Theory 2 Mathematische Zeitschrift 2 Proceedings of the London Mathematical Society. Third Series 2 Ergodic Theory and Dynamical Systems 2 Dynamical Systems 2 Graduate Texts in Mathematics 1 American Journal of Mathematics 1 Compositio Mathematica 1 Journal of Differential Equations 1 Proceedings of the American Mathematical Society 1 Topology 1 Bulletin of the American Mathematical Society 1 Journal of the London Mathematical Society 1 Contemporary Mathematics 1 Lecture Notes in Mathematics
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#### Fields

 26 Measure and integration (28-XX) 18 Dynamical systems and ergodic theory (37-XX) 13 General topology (54-XX) 5 Topological groups, Lie groups (22-XX) 5 Probability theory and stochastic processes (60-XX) 4 Operator theory (47-XX) 2 Ordinary differential equations (34-XX) 2 Functional analysis (46-XX) 1 General and overarching topics; collections (00-XX) 1 Global analysis, analysis on manifolds (58-XX)

#### Citations contained in zbMATH Open

40 Publications have been cited 2,323 times in 2,014 Documents Cited by Year
An introduction to ergodic theory. Zbl 0475.28009
Walters, Peter
1982
An introduction to ergodic theory. Paperback ed. Zbl 0958.28011
Walters, Peter
2000
A variational principle for the pressure of continuous transformations. Zbl 0318.28007
Walters, Peter
1976
Expansive one-parameter flows. Zbl 0242.54041
Bowen, Rufus; Walters, Peter
1972
A relativised variational principle for continuous transformations. Zbl 0388.28020
Ledrappier, Francois; Walters, Peter
1977
Ergodic theory. Introductory lectures. Zbl 0299.28012
Walters, Peter
1975
Invariant measures and equilibrium states for some mappings which expand distances. Zbl 0375.28009
Walters, Peter
1978
Ruelles’s operator theorem and g-measures. Zbl 0331.28013
Walters, Peter
1975
Anosov diffeomorphisms are topologically stable. Zbl 0186.56702
Walters, Peter
1970
On the pseudo orbit tracing property and its relationship to stability. Zbl 0403.58019
Walters, Peter
1978
Convergence of the Ruelle operator for a function satisfying Bowen’s condition. Zbl 1050.37015
Walters, Peter
2001
Equilibrium states for $$\beta$$-transformations and related transformations. Zbl 0364.28016
Walters, Peter
1978
A natural space of functions for the Ruelle operator theorem. Zbl 1122.37017
Walters, Peter
2007
Mildly mixing actions of locally compact groups. Zbl 0523.28021
Schmidt, Klaus; Walters, Peter
1982
Some invariant $$\sigma$$-algebras for measure-preserving transformations. Zbl 0227.28011
Walters, Peter
1972
A dynamical proof of the multiplicative ergodic theorem. Zbl 0765.28014
Walters, Peter
1993
Endomorphisms of a Lebesgue space. Zbl 0232.28013
Parry, William; Walters, Peter
1972
Conjugacy properties of affine transformations of nilmanifolds. Zbl 0207.22801
Walters, Peter
1970
Asymptotic properties of expansive homeomorphisms. Zbl 0176.20701
Bryant, B. F.; Walters, P.
1969
Differentiability properties of the pressure of a continuous transformation on a compact metric space. Zbl 0805.54023
Walters, Peter
1992
Relative pressure, relative equilibrium states, compensation functions and many-to-one codes between subshifts. Zbl 0617.28019
Walters, Peter
1986
Regularity conditions and Bernoulli properties of equilibrium states and $$g$$-measures. Zbl 1069.37021
Walters, Peter
2005
An introduction to the entropy theory of measure-preserving transformations. Zbl 0301.28011
Walters, P.
1974
Topological conjugacy of affine transformations of tori. Zbl 0157.21002
Walters, Peter
1968
Equilibrium states for $$\beta$$-transformations and related transformations. Zbl 0357.28014
Walters, Peter
1978
Some transformations having a unique measure with maximal entropy. Zbl 0319.28011
Walters, Peter
1974
Homeomorphisms with discrete centralizers and ergodic properties. Zbl 0207.22702
Walters, Peter
1970
Minimal skew-product homeomorphisms and coalescence. Zbl 0202.22601
Parry, W.; Walters, P.
1970
Topological conjugacy of affine transformations of compact abelian groups. Zbl 0207.03803
Walters, Peter
1969
Topological Wiener-Wintner ergodic theorems and a random $$L^ 2$$ ergodic theorem. Zbl 0861.28013
Walters, Peter
1996
Some results on the classification of non-invertible measure preserving transformations. Zbl 0257.28011
Walters, Peter
1973
Introductory lectures on ergodic theory. Zbl 0239.28011
Walters, Peter
1970
Roots of n:1 measure-preserving transformations. Zbl 0159.07701
Walters, Peter
1969
The mathematical research of William Parry FRS. Zbl 1134.01317
Pollicott, M.; Sharp, R.; Tuncel, S.; Walters, P.
2008
Symbolic dynamics and its applications. Proceedings of an AMS conference in honor of Roy L. Adler, held at Yale University, New Haven, Connecticut, USA, July 28-August 2, 1991. Zbl 0755.00019
Walters, Peter (ed.)
1992
Unique ergodicity and random matrix products. Zbl 0604.60011
Walters, Peter
1986
On the relationship between zero entropy and quasi-discrete spectrum for affine transformations. Zbl 0177.42001
Walters, Peter
1967
A necessary and sufficient condition for a two-sided continuous function to be cohomologous to a one-sided continuous function. Zbl 1036.37005
Walters, Peter
2003
Erratum to: A necessary and sufficient condition for a two-sided continuous function to be cohomologous to a one-sided continuous function. Zbl 1040.37002
Walters, P.
2003
Affine transformations and coalescence. Zbl 0299.22008
Walters, Peter
1974
The mathematical research of William Parry FRS. Zbl 1134.01317
Pollicott, M.; Sharp, R.; Tuncel, S.; Walters, P.
2008
A natural space of functions for the Ruelle operator theorem. Zbl 1122.37017
Walters, Peter
2007
Regularity conditions and Bernoulli properties of equilibrium states and $$g$$-measures. Zbl 1069.37021
Walters, Peter
2005
A necessary and sufficient condition for a two-sided continuous function to be cohomologous to a one-sided continuous function. Zbl 1036.37005
Walters, Peter
2003
Erratum to: A necessary and sufficient condition for a two-sided continuous function to be cohomologous to a one-sided continuous function. Zbl 1040.37002
Walters, P.
2003
Convergence of the Ruelle operator for a function satisfying Bowen’s condition. Zbl 1050.37015
Walters, Peter
2001
An introduction to ergodic theory. Paperback ed. Zbl 0958.28011
Walters, Peter
2000
Topological Wiener-Wintner ergodic theorems and a random $$L^ 2$$ ergodic theorem. Zbl 0861.28013
Walters, Peter
1996
A dynamical proof of the multiplicative ergodic theorem. Zbl 0765.28014
Walters, Peter
1993
Differentiability properties of the pressure of a continuous transformation on a compact metric space. Zbl 0805.54023
Walters, Peter
1992
Symbolic dynamics and its applications. Proceedings of an AMS conference in honor of Roy L. Adler, held at Yale University, New Haven, Connecticut, USA, July 28-August 2, 1991. Zbl 0755.00019
Walters, Peter (ed.)
1992
Relative pressure, relative equilibrium states, compensation functions and many-to-one codes between subshifts. Zbl 0617.28019
Walters, Peter
1986
Unique ergodicity and random matrix products. Zbl 0604.60011
Walters, Peter
1986
An introduction to ergodic theory. Zbl 0475.28009
Walters, Peter
1982
Mildly mixing actions of locally compact groups. Zbl 0523.28021
Schmidt, Klaus; Walters, Peter
1982
Invariant measures and equilibrium states for some mappings which expand distances. Zbl 0375.28009
Walters, Peter
1978
On the pseudo orbit tracing property and its relationship to stability. Zbl 0403.58019
Walters, Peter
1978
Equilibrium states for $$\beta$$-transformations and related transformations. Zbl 0364.28016
Walters, Peter
1978
Equilibrium states for $$\beta$$-transformations and related transformations. Zbl 0357.28014
Walters, Peter
1978
A relativised variational principle for continuous transformations. Zbl 0388.28020
Ledrappier, Francois; Walters, Peter
1977
A variational principle for the pressure of continuous transformations. Zbl 0318.28007
Walters, Peter
1976
Ergodic theory. Introductory lectures. Zbl 0299.28012
Walters, Peter
1975
Ruelles’s operator theorem and g-measures. Zbl 0331.28013
Walters, Peter
1975
An introduction to the entropy theory of measure-preserving transformations. Zbl 0301.28011
Walters, P.
1974
Some transformations having a unique measure with maximal entropy. Zbl 0319.28011
Walters, Peter
1974
Affine transformations and coalescence. Zbl 0299.22008
Walters, Peter
1974
Some results on the classification of non-invertible measure preserving transformations. Zbl 0257.28011
Walters, Peter
1973
Expansive one-parameter flows. Zbl 0242.54041
Bowen, Rufus; Walters, Peter
1972
Some invariant $$\sigma$$-algebras for measure-preserving transformations. Zbl 0227.28011
Walters, Peter
1972
Endomorphisms of a Lebesgue space. Zbl 0232.28013
Parry, William; Walters, Peter
1972
Anosov diffeomorphisms are topologically stable. Zbl 0186.56702
Walters, Peter
1970
Conjugacy properties of affine transformations of nilmanifolds. Zbl 0207.22801
Walters, Peter
1970
Homeomorphisms with discrete centralizers and ergodic properties. Zbl 0207.22702
Walters, Peter
1970
Minimal skew-product homeomorphisms and coalescence. Zbl 0202.22601
Parry, W.; Walters, P.
1970
Introductory lectures on ergodic theory. Zbl 0239.28011
Walters, Peter
1970
Asymptotic properties of expansive homeomorphisms. Zbl 0176.20701
Bryant, B. F.; Walters, P.
1969
Topological conjugacy of affine transformations of compact abelian groups. Zbl 0207.03803
Walters, Peter
1969
Roots of n:1 measure-preserving transformations. Zbl 0159.07701
Walters, Peter
1969
Topological conjugacy of affine transformations of tori. Zbl 0157.21002
Walters, Peter
1968
On the relationship between zero entropy and quasi-discrete spectrum for affine transformations. Zbl 0177.42001
Walters, Peter
1967
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#### Cited by 1,955 Authors

 27 Ye, Xiangdong 26 Huang, Wen 23 Gelfert, Katrin Grit 21 Pollicott, Mark 19 Sun, Wenxiang 18 Zhao, Yun 17 Chen, Ercai 17 Oprocha, Piotr 16 Cao, Yongluo 16 Urbański, Mariusz 15 Artigue, Alfonso 15 Walters, Peter 14 Feng, De-Jun 14 Mesón, Alejandro M. 14 Varandas, Paulo 14 Vericat, Fernando 13 Amigó, José María 13 Rams, Michał 13 Tian, Xueting 13 Wolf, Christian 13 Zhu, Yujun 12 Cánovas, Jose S. 12 Iommi, Godofredo 12 Li, Zhiming 12 Zhang, Guohua 11 Barreira, Luis Manuel 11 Climenhaga, Vaughn 11 Haydn, Nicolai T. A. 11 Lee, Keonhee 11 Li, Jian 11 Mihailescu, Eugen Gh. 10 Baake, Michael 10 Cheng, Wenchiao 10 Fan, Ai Hua 10 Hofbauer, Franz 10 Huang, Yu 10 Kesseböhmer, Marc 10 Lenz, Daniel H. 10 Lopes, Artur Oscar 10 Pavlov, Ronnie 10 Thompson, Daniel J. 9 Dai, Xiongping 9 Hu, Huyi 8 Downarowicz, Tomasz 8 Kifer, Yuri 8 Kwietniak, Dominik 8 Lee, Manseob 8 Lemańczyk, Mariusz 8 Li, Hanfeng 8 Li, Risong 8 Liao, Gang 8 Ma, Xianfeng 8 Marcus, Brian H. 8 Morales, Carlos Arnoldo 8 Tuncel, Selim 8 Zhou, Shengfan 7 Buzzi, Jérôme 7 Díaz, Lorenzo Justiniano 7 Fernández-Sánchez, Juan 7 Hochman, Michael 7 Keller, Gerhard 7 Keller, Karsten 7 Kennedy, Judy A. 7 Liao, Gongfu 7 Pesin, Yakov Borisovich 7 Quas, Anthony Nicholas 7 Schmidt, Klaus 7 Sharp, Richard W. 7 Snoha, L’ubomír 7 Takahasi, Hiroki 7 Thomsen, Klaus E. 7 Viana, Marcelo 7 Weiss, Benjamin 7 Ye, Yuanling 7 Yuri, Michiko 7 Zheng, Zuohuan 7 Zhou, Yunhua 6 Bambos, Nicholas 6 Bowen, Rufus 6 Boyle, Mike 6 Carrasco-Olivera, Dante 6 Colonius, Fritz 6 de Carvalho, Maria Pires 6 Dikranjan, Dikran N. 6 Frantzikinakis, Nikos 6 Grivaux, Sophie 6 Jaerisch, Johannes 6 Ledrappier, François 6 Li, Jie 6 Lind, Douglas A. 6 Ma, Dongkui 6 Markechová, Dagmar 6 Mcgoff, Kevin 6 Przytycki, Feliks 6 Raith, Peter 6 Shmerkin, Pablo S. 6 Todd, Mike 6 Wang, Shirou 6 Wang, Yangeng 6 Wei, Guo ...and 1,855 more Authors
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#### Cited in 305 Serials

 202 Ergodic Theory and Dynamical Systems 99 Transactions of the American Mathematical Society 80 Discrete and Continuous Dynamical Systems 66 Israel Journal of Mathematics 63 Communications in Mathematical Physics 62 Proceedings of the American Mathematical Society 60 Journal of Statistical Physics 57 Journal of Mathematical Analysis and Applications 53 Journal of Differential Equations 51 Topology and its Applications 42 Advances in Mathematics 41 Chaos, Solitons and Fractals 36 Monatshefte für Mathematik 28 Inventiones Mathematicae 27 Acta Mathematica Sinica. English Series 26 Physica D 24 Journal of Dynamics and Differential Equations 23 Nonlinearity 22 Journal d’Analyse Mathématique 22 Journal of Functional Analysis 20 Mathematische Zeitschrift 19 Indagationes Mathematicae. New Series 19 Dynamical Systems 17 Stochastics and Dynamics 16 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 15 Science China. Mathematics 14 Annales de l’Institut Fourier 14 Discrete and Continuous Dynamical Systems. Series B 12 Fuzzy Sets and Systems 12 Qualitative Theory of Dynamical Systems 12 Entropy 12 Journal of Dynamical Systems and Geometric Theories 11 Probability Theory and Related Fields 11 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 11 Chaos 10 Journal of Mathematical Physics 10 Reports on Mathematical Physics 10 Mathematische Annalen 10 Bulletin of the Brazilian Mathematical Society. New Series 9 Mathematical Proceedings of the Cambridge Philosophical Society 9 Science in China. Series A 9 Stochastic Processes and their Applications 8 Bulletin of the Australian Mathematical Society 8 Duke Mathematical Journal 8 Applied Mathematics. Series B (English Edition) 7 Mathematica Slovaca 7 Theoretical Computer Science 7 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 7 Bulletin of the American Mathematical Society. New Series 7 Journal of Difference Equations and Applications 7 Nonlinear Dynamics 7 Annals of Mathematics. Second Series 7 Journal of Modern Dynamics 6 Letters in Mathematical Physics 6 Applied Mathematics and Computation 6 Journal of Number Theory 6 Mathematical Systems Theory 6 Memoirs of the American Mathematical Society 6 Statistics & Probability Letters 6 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 6 Acta Mathematicae Applicatae Sinica. English Series 6 Journal de Mathématiques Pures et Appliquées. Neuvième Série 6 Bulletin of the American Mathematical Society 5 Annali di Matematica Pura ed Applicata. Serie Quarta 5 Bulletin de la Société Mathématique de France 5 Systems & Control Letters 5 Journal of Theoretical Probability 5 Journal of the American Mathematical Society 5 The Journal of Geometric Analysis 5 Geometric and Functional Analysis. GAFA 5 Aequationes Mathematicae 5 Acta Mathematica Sinica. New Series 5 Journal of Nonlinear Science 5 Journal of Mathematical Sciences (New York) 5 Communications in Nonlinear Science and Numerical Simulation 5 Journal of Dynamical and Control Systems 5 Proceedings of the Steklov Institute of Mathematics 5 Journal of Fractal Geometry 4 Acta Mathematica 4 The Annals of Probability 4 The Annals of Statistics 4 Archiv der Mathematik 4 Czechoslovak Mathematical Journal 4 Functional Analysis and its Applications 4 Integral Equations and Operator Theory 4 Journal of the Korean Mathematical Society 4 Mathematische Nachrichten 4 Proceedings of the Japan Academy. Series A 4 Proceedings of the London Mathematical Society. Third Series 4 Applied and Computational Harmonic Analysis 4 Abstract and Applied Analysis 4 Taiwanese Journal of Mathematics 4 Discrete Dynamics in Nature and Society 4 Annales Henri Poincaré 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Advances in Difference Equations 4 Sahand Communications in Mathematical Analysis 4 Journal de l’École Polytechnique – Mathématiques 3 Computers & Mathematics with Applications 3 Communications on Pure and Applied Mathematics ...and 205 more Serials
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#### Cited in 57 Fields

 1,567 Dynamical systems and ergodic theory (37-XX) 447 Measure and integration (28-XX) 285 General topology (54-XX) 201 Probability theory and stochastic processes (60-XX) 120 Number theory (11-XX) 81 Statistical mechanics, structure of matter (82-XX) 76 Operator theory (47-XX) 60 Differential geometry (53-XX) 59 Functional analysis (46-XX) 49 Ordinary differential equations (34-XX) 47 Computer science (68-XX) 40 Topological groups, Lie groups (22-XX) 40 Information and communication theory, circuits (94-XX) 37 Partial differential equations (35-XX) 34 Quantum theory (81-XX) 33 Global analysis, analysis on manifolds (58-XX) 32 Harmonic analysis on Euclidean spaces (42-XX) 31 Functions of a complex variable (30-XX) 31 Statistics (62-XX) 27 Mathematical logic and foundations (03-XX) 27 Manifolds and cell complexes (57-XX) 23 Several complex variables and analytic spaces (32-XX) 21 Difference and functional equations (39-XX) 21 Systems theory; control (93-XX) 20 Abstract harmonic analysis (43-XX) 19 Group theory and generalizations (20-XX) 19 Convex and discrete geometry (52-XX) 18 Real functions (26-XX) 17 Biology and other natural sciences (92-XX) 16 Combinatorics (05-XX) 15 Numerical analysis (65-XX) 13 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 12 Mechanics of particles and systems (70-XX) 11 Linear and multilinear algebra; matrix theory (15-XX) 11 Fluid mechanics (76-XX) 8 Order, lattices, ordered algebraic structures (06-XX) 8 Approximations and expansions (41-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 7 Algebraic topology (55-XX) 6 Algebraic geometry (14-XX) 5 Optics, electromagnetic theory (78-XX) 4 Relativity and gravitational theory (83-XX) 4 Operations research, mathematical programming (90-XX) 3 History and biography (01-XX) 3 General algebraic systems (08-XX) 3 Field theory and polynomials (12-XX) 3 Commutative algebra (13-XX) 3 Associative rings and algebras (16-XX) 3 Category theory; homological algebra (18-XX) 3 $$K$$-theory (19-XX) 3 Potential theory (31-XX) 3 Geometry (51-XX) 2 Special functions (33-XX) 2 Sequences, series, summability (40-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 General and overarching topics; collections (00-XX) 1 Nonassociative rings and algebras (17-XX)