In my Ph.D. research, I focus on escape dynamics, a central subject in transient dynamics with extensive applications from chemical reactions to celestial mechanics and energy harvesting. Despite numerous studies, the field still poses unresolved questions and remains a rich area for investigation.

Within this domain, I examine conditions such as poly-harmonic excitations and internal damping to understand their effects on the escape mechanisms of particle chains from conservative potential wells. A significant part of my research involves the analytical identification of 'safe basins,' which are regions where particles stay confined under specific excitations. The concept of safe basins serves as an integrity measure, aiding in understanding the dynamics of oscillatory systems.

In addition to my primary focus, I have developed an analytical method in the context of the averaging technique commonly used in nonlinear differential equations. This method substitutes the traditional time average with a space average, employing the classical probability density of the 'fast' variable. The approach also has implications for numerical calculations.