2017, Contemporary mathematics, ISBN 9781470425609, Volume 692., ix, 320 pages

Book

Regular and Chaotic Dynamics, ISSN 1560-3547, 11/2018, Volume 23, Issue 6, pp. 685 - 694

We give a new proof of the existence of compact surfaces embedded in ℝ3 with Anosov geodesic flows. This proof starts with a noncompact model surface whose...

embedded surfaces | cone fields | Anosov flow | 37D40 | 37D20 | Mathematics | 53D25 | Dynamical Systems and Ergodic Theory | geodesic flow | MATHEMATICS, APPLIED | MECHANICS | PHYSICS, MATHEMATICAL | Mathematical research | Mathematics - Dynamical Systems

embedded surfaces | cone fields | Anosov flow | 37D40 | 37D20 | Mathematics | 53D25 | Dynamical Systems and Ergodic Theory | geodesic flow | MATHEMATICS, APPLIED | MECHANICS | PHYSICS, MATHEMATICAL | Mathematical research | Mathematics - Dynamical Systems

Journal Article

Nonlinearity, ISSN 1361-6544, 2008, Volume 21, Issue 4, pp. 677 - 711

...) coincides with the resummation proposed (Baladi 2007) of the (a priori divergent) series Sigma(infinity)(n=0) integral X(y)partial derivative(y)(phi circle f(n)) (y) d mu(0)(y) given by Ruelle's conjecture...

ANALYTICITY | MATHEMATICS, APPLIED | ANOSOV | DYNAMICAL-SYSTEMS | DIFFERENTIABILITY | PHYSICS, MATHEMATICAL | FLUCTUATION-DISSIPATION THEOREM | SRB STATES | Mathematics - Dynamical Systems

ANALYTICITY | MATHEMATICS, APPLIED | ANOSOV | DYNAMICAL-SYSTEMS | DIFFERENTIABILITY | PHYSICS, MATHEMATICAL | FLUCTUATION-DISSIPATION THEOREM | SRB STATES | Mathematics - Dynamical Systems

Journal Article

Nonlinearity, ISSN 1361-6544, 2009, Volume 22, Issue 4, pp. 855 - 870

The classical theory of linear response applies to statistical mechanics close to equilibrium. Away from equilibrium, one may describe the microscopic time...

DIFFEOMORPHISMS | ANALYTICITY | STATISTICAL-MECHANICS | MATHEMATICS, APPLIED | ANOSOV | FAMILIES | SUSCEPTIBILITY | CAUSALITY | PHYSICS, MATHEMATICAL | AXIOM | METRIC ENTROPY | SRB STATES | Physics - Chaotic Dynamics

DIFFEOMORPHISMS | ANALYTICITY | STATISTICAL-MECHANICS | MATHEMATICS, APPLIED | ANOSOV | FAMILIES | SUSCEPTIBILITY | CAUSALITY | PHYSICS, MATHEMATICAL | AXIOM | METRIC ENTROPY | SRB STATES | Physics - Chaotic Dynamics

Journal Article

Ergodic theory and dynamical systems, ISSN 0143-3857, 12/2015, Volume 35, Issue 8, pp. 2669 - 2688

We consider Hölder continuous fiber bunched $\text{GL}(d,\mathbb{R})$-valued cocycles over an Anosov diffeomorphism...

DIFFEOMORPHISMS | MATHEMATICS | MATHEMATICS, APPLIED | CONFORMAL ANOSOV SYSTEMS | LYAPUNOV EXPONENTS | LIE-GROUPS | DYNAMICAL-SYSTEMS | REGULARITY | RIGIDITY | SMOOTH CONJUGACY | LIVSIC THEOREMS | Dynamical systems | Linear equations | Conjugates | Mathematical analysis | Constants | Continuity | Perturbation | Invariants | Fibers | Mathematics - Dynamical Systems

DIFFEOMORPHISMS | MATHEMATICS | MATHEMATICS, APPLIED | CONFORMAL ANOSOV SYSTEMS | LYAPUNOV EXPONENTS | LIE-GROUPS | DYNAMICAL-SYSTEMS | REGULARITY | RIGIDITY | SMOOTH CONJUGACY | LIVSIC THEOREMS | Dynamical systems | Linear equations | Conjugates | Mathematical analysis | Constants | Continuity | Perturbation | Invariants | Fibers | Mathematics - Dynamical Systems

Journal Article

Ergodic theory and dynamical systems, ISSN 0143-3857, 02/2010, Volume 30, Issue 1, pp. 1 - 20

...) and using spaces of bounded p-variation. The first new proof gives differentiability of higher order of ∫ ψ dμ...

ANALYTICITY | MATHEMATICS | MATHEMATICS, APPLIED | GEODESIC-FLOWS | ANOSOV | DYNAMICAL-SYSTEMS | DIFFERENTIABILITY | COLLET-ECKMANN MAPS | POINTS | ENTROPY | Topological manifolds | Theoretical mathematics | Proof theory

ANALYTICITY | MATHEMATICS | MATHEMATICS, APPLIED | GEODESIC-FLOWS | ANOSOV | DYNAMICAL-SYSTEMS | DIFFERENTIABILITY | COLLET-ECKMANN MAPS | POINTS | ENTROPY | Topological manifolds | Theoretical mathematics | Proof theory

Journal Article

Communications in mathematical physics, ISSN 0010-3616, 2012, Volume 314, Issue 3, pp. 689 - 773

We prove exponential decay of correlations for a realistic model of piecewise hyperbolic flows preserving a contact form, in dimension three. This is the first...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | ANOSOV-FLOWS | DIFFEOMORPHISMS | TRANSFER OPERATORS | SOBOLEV SPACES | MAPS | DYNAMICAL-SYSTEMS | BANACH-SPACES | STATISTICAL PROPERTIES | BILLIARD FLOWS | SPECTRUM | PHYSICS, MATHEMATICAL | Dynamical Systems | Chaotic Dynamics | Mathematics | Nonlinear Sciences

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | ANOSOV-FLOWS | DIFFEOMORPHISMS | TRANSFER OPERATORS | SOBOLEV SPACES | MAPS | DYNAMICAL-SYSTEMS | BANACH-SPACES | STATISTICAL PROPERTIES | BILLIARD FLOWS | SPECTRUM | PHYSICS, MATHEMATICAL | Dynamical Systems | Chaotic Dynamics | Mathematics | Nonlinear Sciences

Journal Article

Nonlinearity, ISSN 0951-7715, 06/2008, Volume 21, Issue 6, pp. T81 - T90

Recent results and open problems about the differentiability (or lack thereof) of SRB measures as functions of the dynamics are discussed in this paper.

UNIMODAL MAPS | MATHEMATICS, APPLIED | ANOSOV | DECAY | DYNAMICAL-SYSTEMS | DIFFERENTIABILITY | SPACES | PHYSICS, MATHEMATICAL | SRB STATES

UNIMODAL MAPS | MATHEMATICS, APPLIED | ANOSOV | DECAY | DYNAMICAL-SYSTEMS | DIFFERENTIABILITY | SPACES | PHYSICS, MATHEMATICAL | SRB STATES

Journal Article

Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 11/2016, Volume 36, Issue 11, pp. 6413 - 6451

For a C-2 Axiom A flow phi(t) : M -> M on a Riemannian manifold M and a basic set A for phi(t) we consider the Ruelle transfer operator Lf-s tau+z9, where f...

Zeta function | Axiom A flow | Basic set | Periods counting function | Ruelle transfer operator | ANOSOV-FLOWS | MATHEMATICS | basic set | PERIODIC-ORBITS | MATHEMATICS, APPLIED | ZETA-FUNCTIONS | DECAY | zeta function | periods counting function | AXIOM

Zeta function | Axiom A flow | Basic set | Periods counting function | Ruelle transfer operator | ANOSOV-FLOWS | MATHEMATICS | basic set | PERIODIC-ORBITS | MATHEMATICS, APPLIED | ZETA-FUNCTIONS | DECAY | zeta function | periods counting function | AXIOM

Journal Article

Nonlinearity, ISSN 0951-7715, 03/2011, Volume 24, Issue 3, pp. 699 - 763

Within the abstract framework of dynamical system theory we describe a general approach to the transient (or Evans-Searles) and steady state (or...

MATHEMATICS, APPLIED | ANOSOV | SINAI BILLIARDS | NONEQUILIBRIUM STATIONARY STATES | MARKOV RANDOM-PROCESSES | IRREVERSIBLE-PROCESSES | PHYSICS, MATHEMATICAL | LARGE DEVIATIONS | RECIPROCAL RELATIONS | ENSEMBLES EQUIVALENCE | MATHEMATICAL-THEORY | ANHARMONIC CHAINS | Theorems | Metric space | Fluctuation | Quantum statistics | Mathematical models | Statistical mechanics | Dynamical systems | Steady state | Probability | Operator Algebras | Mathematics | Classical Physics | Mathematical Physics | Physics

MATHEMATICS, APPLIED | ANOSOV | SINAI BILLIARDS | NONEQUILIBRIUM STATIONARY STATES | MARKOV RANDOM-PROCESSES | IRREVERSIBLE-PROCESSES | PHYSICS, MATHEMATICAL | LARGE DEVIATIONS | RECIPROCAL RELATIONS | ENSEMBLES EQUIVALENCE | MATHEMATICAL-THEORY | ANHARMONIC CHAINS | Theorems | Metric space | Fluctuation | Quantum statistics | Mathematical models | Statistical mechanics | Dynamical systems | Steady state | Probability | Operator Algebras | Mathematics | Classical Physics | Mathematical Physics | Physics

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 3/2012, Volume 310, Issue 3, pp. 675 - 704

For hyperbolic flows over basic sets we study the asymptotic of the number of closed trajectories γ with periods T γ lying in exponentially shrinking intervals...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | ANOSOV-FLOWS | ERROR TERMS | HYPERBOLIC FLOWS | DECAY | FOLIATIONS | ORBITS | PHYSICS, MATHEMATICAL | AXIOM | OPEN BILLIARD FLOWS | SYMBOLIC DYNAMICS

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | ANOSOV-FLOWS | ERROR TERMS | HYPERBOLIC FLOWS | DECAY | FOLIATIONS | ORBITS | PHYSICS, MATHEMATICAL | AXIOM | OPEN BILLIARD FLOWS | SYMBOLIC DYNAMICS

Journal Article

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 08/2012, Volume 86, Issue 2, p. 026206

The local density of states (LDOS) is a distribution that characterizes the effects of perturbations on quantum systems. Recently, a semiclassical theory was...

DECOHERENCE | STATES | CHARACTERISTIC VECTORS | DECAY | PHYSICS, FLUIDS & PLASMAS | INFINITE DIMENSIONS | BORDERED MATRICES | SYSTEMS | ANOSOV MAPS | PHYSICS, MATHEMATICAL | ATOM | Quantum Theory | Algorithms | Fourier Analysis | Computer Simulation | Models, Statistical | Nonlinear Dynamics | Physics - methods | Physics - Chaotic Dynamics

DECOHERENCE | STATES | CHARACTERISTIC VECTORS | DECAY | PHYSICS, FLUIDS & PLASMAS | INFINITE DIMENSIONS | BORDERED MATRICES | SYSTEMS | ANOSOV MAPS | PHYSICS, MATHEMATICAL | ATOM | Quantum Theory | Algorithms | Fourier Analysis | Computer Simulation | Models, Statistical | Nonlinear Dynamics | Physics - methods | Physics - Chaotic Dynamics

Journal Article

Acta Mathematica Sinica, English Series, ISSN 1439-8516, 7/2015, Volume 31, Issue 7, pp. 1113 - 1122

Let AC D (M,SL(d,ℝ)) denote the pairs (f,A) so that f ∈ A ⊂ Diff1(M) is a C 1-Anosov transitive diffeomorphisms and A is an SL(d,ℝ...

topological conjugacy | Linear cocycles | 37A20 | Lyapunov exponents | Mathematics, general | Mathematics | 37D25 | maximal entropy measures | 37F15 | Anosov diffeomorphisms | MATHEMATICS | ZERO LYAPUNOV EXPONENTS | MATHEMATICS, APPLIED | INVARIANTS | SYSTEMS | SMOOTH CONJUGACY | Studies | Mathematical analysis | Entropy | Topology | Dynamics | Fibers

topological conjugacy | Linear cocycles | 37A20 | Lyapunov exponents | Mathematics, general | Mathematics | 37D25 | maximal entropy measures | 37F15 | Anosov diffeomorphisms | MATHEMATICS | ZERO LYAPUNOV EXPONENTS | MATHEMATICS, APPLIED | INVARIANTS | SYSTEMS | SMOOTH CONJUGACY | Studies | Mathematical analysis | Entropy | Topology | Dynamics | Fibers

Journal Article

Regular and Chaotic Dynamics, ISSN 1560-3547, 11/2017, Volume 22, Issue 6, pp. 650 - 676

.... We show that if a sequence f n of analytic mappings of C d has a common fixed point f n (0...

37C60 | 34C35 | 37F50 | deformations | scattering theory | 47J07 | 30D05 | Mathematics | Dynamical Systems and Ergodic Theory | nonautonomous linearization | implicit function theorem | MATHEMATICS, APPLIED | MECHANICS | ANOSOV | DYNAMICAL-SYSTEMS | PHYSICS, MATHEMATICAL | SCATTERING | Theorems (Mathematics) | Research | Mathematical research | Mappings (Mathematics)

37C60 | 34C35 | 37F50 | deformations | scattering theory | 47J07 | 30D05 | Mathematics | Dynamical Systems and Ergodic Theory | nonautonomous linearization | implicit function theorem | MATHEMATICS, APPLIED | MECHANICS | ANOSOV | DYNAMICAL-SYSTEMS | PHYSICS, MATHEMATICAL | SCATTERING | Theorems (Mathematics) | Research | Mathematical research | Mappings (Mathematics)

Journal Article

Ergodic theory and dynamical systems, ISSN 0143-3857, 02/2015, Volume 35, Issue 1, pp. 249 - 273

We prove a sharp large deviation principle concerning intervals shrinking with sub-exponential speed for certain models involving the Poincaré map related to a...

ANOSOV-FLOWS | MATHEMATICS | MATHEMATICS, APPLIED | DECAY | MAPS | FOLIATIONS | DYNAMIC-SYSTEMS | TRAJECTORIES | SPECTRA | OPERATORS | AXIOM | OPEN BILLIARD FLOWS | Dynamical systems | Intervals | Axioms | Markov models | Deviation | Regularity | Hyperbolic systems | Ergodic processes | Dynamical Systems | Mathematics | Mathematical Physics | Physics

ANOSOV-FLOWS | MATHEMATICS | MATHEMATICS, APPLIED | DECAY | MAPS | FOLIATIONS | DYNAMIC-SYSTEMS | TRAJECTORIES | SPECTRA | OPERATORS | AXIOM | OPEN BILLIARD FLOWS | Dynamical systems | Intervals | Axioms | Markov models | Deviation | Regularity | Hyperbolic systems | Ergodic processes | Dynamical Systems | Mathematics | Mathematical Physics | Physics

Journal Article

Geometriae Dedicata, ISSN 0046-5755, 8/2016, Volume 183, Issue 1, pp. 181 - 194

In this paper we consider a diffeomorphism f of a compact manifold $$\mathcal {M}$$ M which contracts an invariant foliation W with smooth leaves. If the...

Geometry | Homogeneous structure | Contracting foliation | 37D30 | Normal form | 37D10 | 34C20 | Narrow band spectrum | Mathematics | Polynomial map | MATHEMATICS | SYSTEMS | AUTOMORPHISMS | ANOSOV Z(K) ACTIONS | GLOBAL RIGIDITY | LOCAL RIGIDITY

Geometry | Homogeneous structure | Contracting foliation | 37D30 | Normal form | 37D10 | 34C20 | Narrow band spectrum | Mathematics | Polynomial map | MATHEMATICS | SYSTEMS | AUTOMORPHISMS | ANOSOV Z(K) ACTIONS | GLOBAL RIGIDITY | LOCAL RIGIDITY

Journal Article

Journal of Modern Dynamics, ISSN 1930-5311, 2017, Volume 11, pp. 341 - 368

Let f be a measure-preserving transformation of a Lebesgue space (X, mu) and let F be its extension to a bundle E = X x R-m by smooth fiber maps F-x : E-x -> E...

Homogeneous structure | Contracting foliation | Non-uniform hyperbolicity | Polynomial map | Lyapunov exponents | Normal form | MATHEMATICS | MATHEMATICS, APPLIED | contracting foliation | polynomial map | homogeneous structure | ANOSOV | non-uniform hyperbolicity | FOLIATIONS | Lya-punov exponents | GLOBAL RIGIDITY | LOCAL RIGIDITY

Homogeneous structure | Contracting foliation | Non-uniform hyperbolicity | Polynomial map | Lyapunov exponents | Normal form | MATHEMATICS | MATHEMATICS, APPLIED | contracting foliation | polynomial map | homogeneous structure | ANOSOV | non-uniform hyperbolicity | FOLIATIONS | Lya-punov exponents | GLOBAL RIGIDITY | LOCAL RIGIDITY

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 11/2011, Volume 308, Issue 1, pp. 201 - 225

... from a Hamiltonian microscopic d...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | ANOSOV-FLOWS | CHAIN | TRANSPORT | RANDOM-WALK | MARKOVIAN ENVIRONMENT | MODEL | THERMAL-CONDUCTIVITY | PHYSICS, MATHEMATICAL

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | ANOSOV-FLOWS | CHAIN | TRANSPORT | RANDOM-WALK | MARKOVIAN ENVIRONMENT | MODEL | THERMAL-CONDUCTIVITY | PHYSICS, MATHEMATICAL

Journal Article

Stochastics and Dynamics, ISSN 0219-4937, 04/2018, Volume 18, Issue 2

...) over tilde the corresponding transfer operator. We prove the Dolgopyat inequality for the twisted operator (L) over tilde (s)(v) = (L) over tilde (s) (e(s phi) v...

Semiflow | Mixing rate | Bounded variation | Dolgopyat inequality | bounded variation | ANOSOV-FLOWS | INDIFFERENT FIXED-POINTS | INTERVAL MAPS | EXPONENTIAL DECAY | semiflow | STATISTICS & PROBABILITY | mixing rate

Semiflow | Mixing rate | Bounded variation | Dolgopyat inequality | bounded variation | ANOSOV-FLOWS | INDIFFERENT FIXED-POINTS | INTERVAL MAPS | EXPONENTIAL DECAY | semiflow | STATISTICS & PROBABILITY | mixing rate

Journal Article

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