The main aim of this paper is to identify and evaluate the use of nonlinear methods of analysis of dynamic economic processes represented by one-dimensional time series and observe the state of their behavior to study the investment attractiveness of jointstock companies on the Warsaw Stock Exchange. The study uses chaos theory as one of the novel methods of describing capital markets, which is an advantage over the classic methods of capital market analysis and describes how it functions as a linear system. The fractal analysis of selected companies listed on the Warsaw Stock Exchange detected the existence of long-term memory. Joint-stock companies on the Polish stock exchange have positive Lyapunov exponents, fractal dimensions in the form of fractional numbers, and therefore, the possibility of examining deterministic chaos using tools. The price charts of companies’ shares indicate that these are not straight lines but lines that form a zig-zag shape, characteristic for nonlinear systems. Research shows that the Polish capital market has fractal properties, and thus analysis using deterministic chaos methods is possible.