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In this work we study strong spectral properties of Ruelle transfer operators related to a large family of Gibbs measures for contact Anosov flows. The ultimate aim is to establish exponential decay of correlations for Hölder observables with respect to a very general class of Gibbs measures. The approach invented in 1997 by Dolgopyat in “On decay of correlations in Anosov flows” and further developed in Stoyanov (2011) is substantially refined here, allowing to deal with much more general situations than before, although we still restrict ourselves to the uniformly hyperbolic case. A rather general procedure is established which produces the desired estimates whenever the Gibbs measure admits a Pesin set with exponentially small tails, that is a Pesin set whose preimages along the flow have measures decaying exponentially fast. We call such Gibbs measures regular. Recent results in Gouëzel and Stoyanov (2019) prove existence of such Pesin sets for hyperbolic diffeomorphisms and flows for a large variety of Gibbs measures determined by Hölder continuous potentials. The strong spectral estimates for Ruelle operators and well-established techniques lead to exponential decay of correlations for Hölder continuous observables, as well as to some other consequences such as: (a) existence of a non-zero analytic continuation of the Ruelle zeta function with a pole at the entropy in a vertical strip containing the entropy in its interior; (b) a Prime Orbit Theorem with an exponentially small error.

We develop cohomological interpretations for several types of automorphic forms for Hecke triangle groups of infinite covolume. We then use these interpretations to establish explicit isomorphisms between spaces of automorphic forms, cohomology spaces and spaces of eigenfunctions of transfer operators. These results show a deep relation between spectral entities of Hecke surfaces of infinite volume and the dynamics of their geodesic flows.

We show that the linear drift of the Brownian motion on the universal cover of a closed connected smooth Riemannian manifold is

This paper is an interval dynamics counterpart of three theories founded earlier by the authors, S. Smirnov and others in the setting of the iteration of rational maps on the Riemann sphere: the equivalence of several notions of non-uniform hyperbolicity, Geometric Pressure, and Nice Inducing Schemes methods leading to results in thermodynamical formalism. We work in a setting of generalized multimodal maps, that is smooth maps

The growing problems of excessive vibration in steel structures due to human rhythmic activities and vibrating machinery have led to the need for increasingly rigorous dynamic analysis in order to verify excessive displacements and ensure the users’ comfort. The present work aimed to carry out, via numerical simulation in ANSYS Mechanical APDL software, static, modal and harmonic analysis in steel frames with two floors and two bays in order to investigate the influence of the connection’s stiffness on the behavior of the structure. The results obtained showed that the natural frequency value of the models increases as the stiffness of the beam-column connections is increased. However, due to the harmonic analysis performed, it was not possible to delineate a behavior between the stiffness of the connections and the amplification.

We develop a comprehensive theory of conformal graph directed Markov systems in the non-Riemannian setting of Carnot groups equipped with a sub-Riemannian metric. In particular, we develop the thermodynamic formalism and show that, under natural hypotheses, the limit set of an Carnot conformal GDMS has Hausdorff dimension given by Bowen’s parameter. We illustrate our results for a variety of examples of both linear and nonlinear iterated function systems and graph directed Markov systems in such sub-Riemannian spaces. These include the Heisenberg continued fractions introduced by Lukyanenko and Vandehey as well as Kleinian and Schottky groups associated to the non-real classical rank one hyperbolic spaces.

In this monograph we consider the general setting of conformal graph directed Markov systems modeled by countable state symbolic subshifts of finite type. We deal with two classes of such systems: attracting and parabolic. The latter being treated by means of the former. We prove fairly complete asymptotic counting results for multipliers and diameters associated with preimages or periodic orbits ordered by a natural geometric weighting. We also prove the corresponding Central Limit Theorems describing the further features of the distribution of their weights. These results have direct applications to a wide variety of examples, including the case of Apollonian Circle Packings, Apollonian Triangle, expanding and parabolic rational functions, Farey maps, continued fractions, Mannenville-Pomeau maps, Schottky groups, Fuchsian groups, and many more. This gives a unified approach which both recovers known results and proves new results. Our new approach is founded on spectral properties of complexified Ruelle–Perron–Frobenius operators and Tauberian theorems as used in classical problems of prime number theory.

This volume is a tribute to one of the founders of modern theory of dynamical systems, the late Dmitry Victorovich Anosov.It contains both original papers and surveys, written by some distinguished experts in dynamics, which are related to important themes of Anosov's work, as well as broadly interpreted further crucial developments in the theory of dynamical systems that followed Anosov's original work.Also included is an article by A. Katok that presents Anosov's scientific biography and a picture of the early development of hyperbolicity theory in its various incarnations, complete and partial, uniform and nonuniform.

A threshing drum in a power thresher has a main function for separating seeds from stems via threshing teeth. This part undergoes with high exposure of vibrations, which has a greater chance to work improperly and experiences a fatigue failure that can reduce the efficiency. The main objective of this paper is to obtain vibration characteristics of the proposed design of the threshing drum. In order to achieve the objective, the threshing drum is to be modeled as an equivalent spring and a mass, which is coupled in series mode with equivalent springs and dampers generated from bearings. The mathematical models of the system are derived only in vertical direction. The transfer function approach is established to obtain time and frequency domain analysis. Force and displacement transmissibility are plotted in the wide range of frequencies to perform transmitted force to the main frame, while vertical vibration exposures are evaluated based on ISO 2372. The result shows that the threshing drum design is in the good criterion that means the Root Means Square of the velocity lyingfrom 0.11 m/s to 2.8 m/s taken from vibration severity index in the range of 400 rpm to 1000 rpm.

Dynamic process modeling is essential for simulating time‐evolving biochemical systems, particularly those with multistate interactions and combinatorial complexity. Traditional Ordinary Differential Equation (ODE) models offer mechanistic clarity but struggle with scalability and context‐sensitive encoding. Rule‐Based Modeling (RBM) frameworks address these limitations through modular rule ion, yet require manual specification and lack adaptive learning. This study introduces algorithmic innovations within the Neural Ordinary Differential Equation (Neural ODE) paradigm to bridge the gap between mechanistic interpretability and scalable expressivity. Neural ODEs can be considered as a revolutionary approach in the field of modeling dynamic biochemical interactions. They have made it possible to create models of such interactions that are flexible enough to adapt to different scenarios and do so without requiring any manual intervention in terms of rule encoding or predefined reaction schemes. This is achieved by employing differential solvers within the framework of neural networks, thus enabling a learning process that is in accordance with the behavior of the system. Using the DARPP‐32 signaling network—a benchmark system characterized by multivalent phosphorylation and dynamic perturbations—the proposed Neural ODE framework demonstrates the ability to replicate key dynamic behaviors observed in ODE and RBM models. Comparative simulations under baseline and perturbed conditions reveal that Neural ODEs maintain trajectory fidelity while offering enhanced modularity and computational efficiency. Feature importance analysis and latent space visualizations further validate the model's interpretability and robustness. Unlike ODEs and RBMs, Neural ODEs adapt to structural mutations and binding schemes through latent trajectory learning, enabling flexible simulation of biochemical variability without manual rule encoding. This work establishes Neural ODEs as a viable and scalable alternative for modeling complex biochemical systems, combining the strengths of data‐driven learning with the interpretability of differential equations. This study presents algorithmic innovations in Neural Ordinary Differential Equations (NeuralODEs) for dynamic process modeling of complex biochemical systems. Using the DARPP‐32 signaling network as a benchmark, the proposed framework demonstrates accurate replication of ODE and Rule‐Based Model behaviors while offering enhanced modularity, computational efficiency, and adaptability to structural variations. Feature importance analysis and latent trajectory learning highlight the model's interpretability and robustness, establishing NeuralODEs as a scalable alternative for simulating multistate biochemical dynamics.