Donald Samuel Ornstein

Donald Samuel Ornstein's AcademicInfluence.com Rankings

Mathematics

#2058

World Rank

#3236

Historical Rank

#824

USA Rank

Measure Theory

#715

World Rank

#964

Historical Rank

#284

USA Rank

mathematics Degrees

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Mathematics

Donald Samuel Ornstein's Degrees

PhD Mathematics University of California, Berkeley

Why Is Donald Samuel Ornstein Influential?

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According to Wikipedia, Donald Samuel Ornstein is an American mathematician working in the area of ergodic theory. He received a Ph.D. from the University of Chicago in 1957 under the guidance of Irving Kaplansky. During his career at Stanford University he supervised the Ph. D. thesis of twenty three students, including David H. Bailey, Bob Burton, Doug Lind, Ami Radunskaya, Dan Rudolph, and Jeff Steif.

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Donald Samuel Ornstein's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Entropy and isomorphism theorems for actions of amenable groups (1987) (564)
Ergodic theory, randomness, and dynamical systems (1974) (473)
Bernoulli shifts with the same entropy are isomorphic (1970) (415)
Ergodic theory of amenable group actions. I: The Rohlin lemma (1980) (344)
Entropy and data compression schemes (1993) (282)
On isomorphism of weak Bernoulli transformations (1970) (196)
A non-inequality for differential operators in the L1 norm (1962) (191)
The ergodic theoretical proof of Szemerédi's theorem (1982) (184)
Billiards and Bernoulli schemes (1974) (170)
On the root problem in ergodic theory (1972) (159)
Equivalence of measure preserving transformations (1982) (148)
Two Bernoulli shifts with infinite entropy are isomorphic (1970) (147)
A general ergodic theorem (1960) (146)
On invariant measures (1960) (136)
How Sampling Reveals a Process (1990) (123)
Geodesic flows are Bernoullian (1973) (111)
The Shannon-McMillan-Breiman theorem for a class of amenable groups (1983) (108)
An Application of Ergodic Theory to Probability Theory (1973) (107)
Factors of Bernoulli shifts are Bernoulli shifts (1970) (99)
Statistical properties of chaotic systems (1991) (97)
The absolute continuity of the conjugation of certain diffeomorphisms of the circle (1989) (85)
On the Bernoulli nature of systems with some hyperbolic structure (1998) (83)
The differentiability of the conjugation of certain diffeomorphisms of the circle (1989) (80)
An Operator Theorem on $L_1$ Convergence to Zero with Applications to Markov Kernels (1970) (76)
On the existence of stationary optimal strategies (1969) (72)
Guessing the next output of a stationary process (1978) (69)
Ergodic Theory, Randomness, and "Chaos" (1989) (68)
Universal Almost Sure Data Compression (1990) (67)
An uncountable family of K-automorphisms (1973) (64)
Cutting and stacking, interval exchanges and geometric models (1985) (61)
Imbedding Bernoulli shifts in flows (1970) (57)
An example of a Kolmogorov automorphism that is not a Bernoulli shift (1973) (51)
Semi-rigidity of horocycle flows over compact surfaces of variable negative curvature (1987) (49)
Finitely determined implies very weak Bernoulli (1974) (47)
Random walks. I (1969) (47)
Nonblock Source Coding with a Fidelity Criterion (1975) (44)
Appendix on return-time sequences (1989) (43)
On the Pointwise Behavior of Iterates of a Self-Adjoint Operator (1968) (37)
Every transformation is bilaterally deterministic (1975) (34)
Block coding for discrete stationary d -continuous noisy channels (1979) (34)
The isomorphism theorem for Bernoulli flows (1973) (32)
A remark on the Birkhoff ergodic theorem (1971) (28)
Entropy and recurrence rates for stationary random fields (1994) (28)
Sliding-block joint source/noisy-channel coding theorems (1976) (28)
A K automorphism with no square root and Pinsker's conjecture (1973) (28)
Block Synchronization, Sliding-Block Coding, Invulnerable Sources and Zero Error Codes for Discrete Noisy Channels (1980) (23)
A mixing transformation for which Pinsker's conjecture fails (1973) (22)
Mixing Markov shifts of kernel type are Bernoulli (1973) (22)
On the recurrence of sums of random variables (1962) (21)
Factors of Bernoulli shifts (1975) (21)
Random walks. II (1969) (20)
Newton's laws and coin tossing (2013) (19)
On mixing and partial mixing (1972) (19)
Entropy is the Only Finitely Observable Invariant (2006) (19)
Subsequence ergodic theorems for amenable groups (1992) (19)
Ergodic transformations induce mixing transformations (1973) (17)
Some new results in the Kolmogorov-Sinai theory of entropy and ergodic theory (1971) (17)
Continuous speed changes for flows (1978) (15)
Twist Maps and Aubry-Mather Sets (2003) (15)
The d-Recognition of Processes (1994) (11)
Ergodic flows of positive entropy can be time changed to becomeK-flows (1977) (11)
A limit theorem for independent random variables (1967) (11)
Unilateral codings of Bernoulli systems (1975) (10)
Dual Vector Spaces (1959) (9)
Return times of dynamical systems (1989) (8)
What does it mean for a mechanical system to be isomorphic to the Bernoulli flow (1975) (8)
The differentiability of transition functions (1960) (7)
MEASURE-PRESERVING TRANSFORMATIONS AND RANDOM PROCESSES (1971) (6)
A new method for twist theorems (1993) (6)
On the existence of a σ-finite invariant measure under a generalized Harris condition (1970) (5)
Any flow is an orbit factor of any flow (1984) (5)
A new proof of the paracompactness of metric spaces (1969) (5)
A general property of random walk (1962) (5)
ON A THEOREM OF OREY (1969) (3)
Discussion on Professor Ornstein's Paper (1973) (2)
In what sense can a deterministic system be random (1995) (2)
Ornstein theory (2008) (2)
A characterization of monotone functions (1971) (2)
Some Open Problems in Ergodic Theory (1975) (2)
Kolmogorov, random processes, and Newtonian dynamics (2004) (1)
ISOMETRIES OF ORLICZ SPACES BY (2007) (1)
Problems in Ergodic Theory (2018) (0)
Problems in Ergodic Theory (2018) (0)
The isomorphism problem in ergodic theory (1970) (0)
The purpose of this paper is to generalize a theorem of Spitzer and Kesten (2010) (0)
Mechanical systems and random processes (1977) (0)
Boltzmann, ergodic theory, and chaos (2008) (0)
Smoothness of Invariant Curves (2020) (0)
UNILATERAL CODINGS OF (1975) (0)

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Donald Samuel Ornstein's Academic­Influence.com Rankings