Multivariate multifractal analysis of Lévy functions. Part I: Determination of multifractal spectra

Key Points

• This research aims to identify points where Lévy functions intersect based on Hölder exponents and to analyze their dimensions.
• Studied sets of points for Lévy functions and their translations.
• Examined the relationship between Hölder exponents and Hausdorff dimensions.
• Analyzed the manner in which dimensions depend on the translation parameter.
• Found specific conditions under which Lévy functions share Hölder exponents.
• Demonstrated a correlation between translation parameter and Hausdorff dimensions.
• Identified the nature of multifractal spectra for the examined functions.