TY  - BOOK
AU  - Bhattacharya,Siddhartha
AU  - Das,Tarun
AU  - Ghosh,Anish
AU  - Shah,Riddhi
TI  - Recent Trends in Ergodic Theory and Dynamical Systems
T2  - Contemporary Mathematics
SN  - 9781470422196
AV  - QA614.8 -- .R434 2015eb 
U1  - 515/.48 
PY  - 2015///
CY  - Providence
PB  - American Mathematical Society
KW  - Dani, S. G
KW  - Differentiable dynamical systems -- Congresses
KW  - Ergodic theory -- Congresses
KW  - Mathematical analysis -- Congresses
KW  - Electronic books
N1  - Cover -- Title page -- Contents -- Preface -- S. G. Dani as I have known him -- Cubic averages and large intersections -- 0. Introduction -- 1. The Fubini principle -double and repeated Cesàro limits -- 2. Large cubic averages: proof of Theorem 0.6 -- 3. Furstenberg's correspondence principle for general amenable groups and its applications -- References -- Liouville property on   -spaces -- 1. Introduction -- 2. Preliminaries -- 3. Actions on vector spaces -- 4. Actions on projective spaces -- 5. Miscellaneous remarks -- 6. Examples -- References -- A new connection between metric theory of Diophantine approximations and distribution of algebraic numbers -- 1. Introduction -- 2. Effective theorems in metric theory of Diophantine approximations of dependent variables -- 3. Distribution of conjugate algebraic numbers -- 4. Distribution of resultants of integral polynomials -- 5. Distribution of discriminants of integral polynomials -- 6. Algebraic numbers in small intervals -- References -- The gap distribution of slopes on the golden L -- 1. Introduction -- 2. Strata, \SL(2,\R)-action, and Veech groups -- 3. Horocycle flows and first return maps -- 4. Ergodicity and equidistribution -- 5. Further questions -- A. Explicit formulas for the probability distribution function -- B. Volume computations -- C. Quadratic Asymptotics -- References -- Uniformly recurrent subgroups -- Introduction -- 1. Stability systems -- 2. Homogeneity properties of a URS -- 3. URS's for Wreath products -- 4. Applications to ergodic systems -- 5. Uncountably many URS's for   ₂ -- 6. Realizations of URS's as stability systems -- References -- Values of binary quadratic forms at integer points and Schmidt games -- 1. Introduction -- 2. Dynamics and gaps between values of quadratic forms -- 3. Schmidt games -- 4. Transversality and reduction to discrete time actions; 5. Completion of the proof: the percentage game -- References -- Conformal families of measures for general iterated function systems -- 1. Introduction -- 2. Iterated Function Systems -- 3. Conformal Measures -- References -- Dani's work on probability measures on groups -- 1. Introduction to the embedding problem -- 2. The embedding problem on connected Lie groups -- 3. A basic technique and its applications -- 4. Recent results on the embedding problem on Lie groups -- 5. The embedding problem on general locally compact groups -- References -- On the homogeneity at infinity of the stationary probability for an affine random walk -- 1. Introduction -- 2. Calculation of invariant measures on ℝ in a special case -- 3. Proof of Theorem 1.1 -- 4. Appendix -- References -- Dani's work on dynamical systems on homogeneous spaces -- 1. Unipotent flows -- 2. Applications in Number Theory -- 3. Dynamics of non-unipotent homogeneous flows -- References -- Calculus of generalized Riesz products -- 1. Introduction -- 2. Generalized Riesz Products and their Weak Dichotomy -- 3. Outer Polynomials and Mahler Measure -- 4. A Formula for Radon Nikodym Derivative -- 5. A Conditional Strong Dichotomy and Other Discussion -- 6. Non-Singular Rank One Maps and Flat Polynomials -- 7. Zeros of Polynomials -- References -- Diophantine approximation exponents on homogeneous varieties -- 1. Introduction -- 2. Diophantine approximation and the shrinking target property -- 3. Diophantine exponents for group actions -- 4. Examples of Diophantine exponents -- References -- Ergodicity of principal algebraic group actions -- 1. Principal Algebraic Group Actions -- 2. Cohomological results -- 3. Ergodicity of principal actions -- References -- A note on three problems in metric Diophantine approximation -- 1. Multiplicatively   -well approximable points; 2. Diophantine approximation on planar curves -- 3. Inhomogeneous badly approximable points -- References -- Dynamical invariants for group automorphisms -- 1. Introduction -- 2. Algebraic isomorphism -- 3. Topological conjugacy -- 4. Measurable isomorphism -- 5. One-solenoids and subgroups of the rationals -- 6. Counting closed orbits -- References -- Back Cover
UR  - https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114308
ER  -