Related papers: Specification and Thermodynamic Properties of Topo…
The dynamics of symbolic systems, such as multidimensional subshifts of finite type or cellular automata, are known to be closely related to computability theory. In particular, the appropriate tools to describe and classify topological…
We investigate the relationship between various topological pressures and the corresponding measure-theoretic pressures for nonautonomous dynamical systems based on the Carath\'eodory-Pesin structure. We prove a pressure distribution…
A general method for constructing simplicial complex from observed time series of dynamical systems based on the delay coordinate reconstruction procedure is presented. The obtained simplicial complex preserves all pertinent topological…
Predicting the dynamical properties of topological matter is a challenging task, not only in theoretical and experimental settings, but also numerically. This work proposes a variational approach based on a time-dependent correlated Ansatz,…
For a locally compact sofic group continuously acting on a compact metric space, we first study the relative sofic entropy and prove an additive inequality relating sofic entropy and relative sofic entropy. Moreover, it is shown that the…
We develop a quenched thermodynamic formalism for a wide class of random maps with non-uniform expansion, where no Markov structure, no uniformly bounded degree or the existence of some expanding dynamics is required. We prove that every…
In this paper, we consider measure-theoretical restricted sensitivity and topological restricted sensitivities by restricting the first sensitive time. For a given topological dynamical system, we define measure-theoretical restricted…
In this paper we extend the notion of a continuous bundle random dynamical system to the setting where the action of $\R$ or $\N$ is replaced by the action of an infinite countable discrete amenable group. Given such a system, and a…
We consider some local entropy properties of dynamical systems under the assumption of shadowing. In the first part, we give necessary and sufficient conditions for shadowable points to be certain entropy points. In the second part, we give…
For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a…
We construct suitable metrics for two classes of topological dynamical systems (linear maps on the torus and non-invertible expansive maps on compact spaces) in order to get a lower bound for topological entropy in terms of the resulting…
In this work we study the main dynamical properties of the push-forward map, a transformation in the space of probabilities P(X) induced by a map T: X \to X, X a compact metric space. We also establish a connection between topological…
We survey the connections between entropy, chaos, and independence in topological dynamics. We present extensions of two classical results placing the following notions in the context of symbolic dynamics: 1. Equivalence of positive entropy…
The limit of small entropy production is reached in relaxing systems long after preparation, and in stationary driven systems in the limit of small driving power. Surprisingly, for extended systems this limit is not in general the…
Different notions of entropy play a fundamental role in the classical theory of dynamical systems. Unlike many other concepts used to analyze autonomous dynamics, both measure-theoretic and topological entropy can be extended quite…
Many dynamical phenomena in complex systems concern spreading that plays out on top of networks with changing architecture over time -- commonly known as temporal networks. A complex system's proneness to facilitate spreading phenomena,…
For a dynamical system satisfying the approximate product property and asymptotically entropy expansiveness, we characterize a delicate structrue of the space of invariant measures: The ergodic measures of intermediate entropies and…
In this thesis, we provide an initial investigation into bounds for topological entropy of switched linear systems. Entropy measures, roughly, the information needed to describe the behavior of a system with finite precision on finite time…
Topological dynamics constitutes the study of asymptotic properties of orbits under flows or maps on the Hausdorff phase space. Hyperbolic dynamics is the study of differentiable flows or maps that are usually characterized by the presence…
In this work we study the problem of positiveness of topological entropy for flows using pointwise dynamics. We show that the existence of a non-periodic nonwandering point of an expansive and non-singular flow with shadowing is a…