9 papers
Statistical Limit Theorems for Axiom A Diffeomorphisms: Exponential Mixing, Central Limit Theorem, and Large Deviations
Abdoulaye Thiam
We establish statistical limit theorems for equilibrium states of Axiom A diffeomorphisms, derived from the spectral gap of the Ruelle transfer operator established in Part I (Thia…
Transfer Operators and SRB Measures for Axiom A Diffeomorphisms: Spectral Gap, Structural Stability, and the Gibbs Equivalence Theorem
Abdoulaye Thiam
We develop the Ruelle transfer operator theory for Axiom A diffeomorphisms and construct Sinai-Ruelle-Bowen measures, carrying the symbolic spectral results of Part I [64] over to…
Mixed Global Dynamics of the Forced Vibro-Impact Oscillator with Coulomb Friction and its Symplectic Structure, KAM Tori, and Persistence
Abdoulaye Thiam
The forced vibro-impact oscillator with Amonton-Coulomb friction and elastic walls was shown by Gendelman et al. (2019) to exhibit a coexistence of Hamiltonian stability islands an…
Quantitative Analyticity for Lyapunov Exponents of Random Products of Matrices with Explicit Polydiscs and Cauchy Coefficient Bounds
Abdoulaye Thiam
The top Lyapunov exponent of a random product of matrices in , , with simple top spectrum, depends real-analytically on the probab…
Quantitative Hölder Regularity, Concentration, and Spectral Applications for Lyapunov Exponents of Random Cocycles, with Extensions to
Abdoulaye Thiam
This paper develops a quantitative regularity theory for the Lyapunov exponents of random products of matrices in , with extensions to $\operatorna…
Multifractal Analysis, Livšic Rigidity, and Fluctuation Theorems for Axiom A Diffeomorphisms: The Pesin Formula and the Gallavotti-Cohen Symmetry
Abdoulaye Thiam
This Part develops structural consequences of the thermodynamic formalism for Axiom A diffeomorphisms. The Pesin Entropy Formula equates the metric entropy of the SRB measure to th…
Uniform Hyperbolicity and Symbolic Dynamics: Markov Partitions, Shadowing, and the Coding of Axiom A Diffeomorphisms
Abdoulaye Thiam
This Part establishes the geometric theory of uniformly hyperbolic sets with explicit quantitative bounds throughout, and contains five main theorems. The Stable Manifold Theorem i…
The Convex-Analytic Structure of Thermodynamic Equilibrium: Pressure, Subdifferentials, and Phase Transitions
Abdoulaye Thiam
We develop the convex-analytic structure of the thermodynamic formalism for continuous maps on compact metric spaces. The pressure functional is the Legendre-Fenchel transform of t…
Gibbs Measures on Subshifts of Finite Type: Five Equivalent Characterizations with Explicit Constants
Abdoulaye Thiam
We prove that five characterizations of Gibbs measures for Hölder potentials on topologically mixing subshifts of finite type are equivalent: the Jacobian condition, the classical…