The article investigates the chaotic properties of weighted displacement operators acting on (non-separable) Hilbert space, which is one of the important objects in the theory of dynamical systems. Particular attention is paid to the analysis of the conditions under which such operators can be topologically transitive, hypercyclic and often hypercyclic. In addition, the phenomenon of Lee-York chaos is investigated, which implies the existence of uncountable sets of points with chaotic behavior of orbits. This allows for a deeper understanding of the nature of dynamical systems characterized by irregularity and unpredictability.The article investigates the chaotic properties of weighted displacement operators acting on (non-separable) Hilbert space, which is one of the important objects in the theory of dynamical systems. Particular attention is paid to the analysis of the conditions under which such operators can be topologically transitive, hypercyclic, and often hypercyclic. In addition, the phenomenon of Lee-York chaos is investigated, which implies the existence of uncountable sets of points with chaotic behavior of orbits. This allows for a deeper understanding of the nature of dynamical systems characterized by irregularity and unpredictability. The article highlights how different properties of weighted shift operators affect their dynamic behavior, considering the interaction between the operator weights and the structure of the underlying space. For illustration, two examples of dynamical systems are proposed that can be used to model price behavior in financial markets. The first example is based on a simple linear model, where the price change is proportional to the current value. The orbit constructed in this example is not dense in the general case. The second example models a more complex system that takes into account the dependence of the price change on previous values, dividends, and random factors. In this context, the weighted shift operator plays a key role, allowing the creation of a hypercyclic dynamic system capable of adequately reflecting chaotic price behavior. The application of chaos theory to financial markets is particularly relevant, as it allows taking into account complex dynamics, nonlinearity, and the influence of random factors on price changes. The use of such models can help investors better understand the nature of risks, find investment opportunities, and make more informed decisions under uncertainty. The results obtained are also important for a wide range of scientific research in the fields of mathematics, physics, and economics, where the study of chaotic properties of systems is central to understanding their behavior.

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