Editorial — Leonid Pavlovich Shilnikov

Abstract

This special issue presents a selection of papers from the conference “Dynamics, Bifurcations and Strange Attractors” dedicated to the memory of Leonid Pavlovich Shilnikov (1934–2011) to commemorate his contributions to the theory of dynamical systems and bifurcations. The conference was held at the Lobachevsky State University of Nizhny Novgorod, Russia, on 1–5 July 2013. The conference was attended by 155 participants from all over the world, who contributed to the three focal topics: bifurcations and strange attractors; dynamical systems with additional structures (Hamiltonian, time-reversible, etc.); applications of dynamical systems. The topics were chosen in confluence with pivotal contributions by L. P. Shilnikov to the fields. The speakers presented their current research and outlined future directions in both theory and frontier applications. The organizers of the conference are grateful to its sponsors: Russian Foundation of Basic Research, D. Zimin’s Russian Charitable Foundation “Dynasty,” R&D company Mera-NN, and K. V. Kirsenko (Russia), as well as Office of Naval Research (USA) and its officers, Drs. M. Harper (UK) and M. Shlesinger (USA). We thank the Editors-in-Chief of the International Journal of Bifurcations and Chaos: Ron Chen and Leon Chua for having the proceedings published here. L. P. Shilnikov served on the Editorial Board of the journal from the time it was founded. Our dear friend, mentor and fellow researcher, L. P. Shilnikov conceptualized the theory of global bifurcations of high-dimensional systems and was one of the founders of the mathematical theory of dynamical chaos. He built a profound research school in the city of Nizhny Novgorod (Gorky formerly) — the Shilnikov School that continues to this day. His works greatly influenced the overall development of the mathematical theory of dynamical systems as well as nonlinear dynamics, in general. Shilnikov’s findings have been included in most textand reference books, and are used worldwide by mathematics students and nonlinear dynamists to study the qualitative theory of dynamical systems and chaos. The elegance and completeness of his results let them reach “the heart of the matter,” and provide applied researchers with an in-depth mathematical understanding of the outcomes of natural experiments. The popularity and appreciation are due to the “living classic” status attained by Professor Shilnikov over several decades of his life through continuous hard work on bifurcation theory of multidimensional dynamical systems, mathematical chaos theory and theory of strange attractors. L. P. Shilnikov was born in Kotelnich, Kirov region of Russia on December 17, 1934. After graduating from a local high school in 1952, he became a student in the Department of Physics and Mathematics at Gorky State University. After graduation in 1957, he continued his PhD studies at the same university. He defended his PhD thesis “On birth of stable periodic orbits from singular trajectories” in 1962, it focused on the multidimensional generalization of basic homoclinic bifurcations, which were originally discovered and studied for systems on a plane by A. A. Andronov and E. A. Leontovich in the early 1930s.