Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have completely random states of disorder and irregularities. Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals, and self-organization. The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state. A metaphor for this behavior is that a butterfly flapping its wings in Brazil can cause a tornado in Texas.
Aleksandr Mikhailovich Lyapunov was a Russian mathematician, mechanician and physicist. His surname is variously romanized as Ljapunov, Liapunov, Liapounoff or Ljapunow. He was the son of the astronomer Mikhail Lyapunov and the brother of the pianist and composer Sergei Lyapunov.
Rudolf Emil Kálmán was a Hungarian-American electrical engineer, mathematician, and inventor. He is most noted for his co-invention and development of the Kalman filter, a mathematical algorithm that is widely used in signal processing, control systems, and guidance, navigation and control. For this work, U.S. President Barack Obama awarded Kálmán the National Medal of Science on October 7, 2009.
Richard Ernest Bellman was an American applied mathematician, who introduced dynamic programming in 1953, and made important contributions in other fields of mathematics, such as biomathematics. He founded the leading biomathematical journal Mathematical Biosciences.
Fundamenta Mathematicae is a peer-reviewed scientific journal of mathematics with a special focus on the foundations of mathematics, concentrating on set theory, mathematical logic, topology and its interactions with algebra, and dynamical systems.
Yakov Grigorevich Sinai is a Russian-American mathematician known for his work on dynamical systems. He contributed to the modern metric theory of dynamical systems and connected the world of deterministic (dynamical) systems with the world of probabilistic (stochastic) systems. He has also worked on mathematical physics and probability theory. His efforts have provided the groundwork for advances in the physical sciences.
Society for Industrial and Applied Mathematics (SIAM) is a professional society dedicated to applied mathematics, computational science, and data science through research, publications, and community. SIAM is the world's largest scientific society devoted to applied mathematics, and roughly two-thirds of its membership resides within the United States. Founded in 1951, the organization began holding annual national meetings in 1954, and now hosts conferences, publishes books and scholarly journals, and engages in advocacy in issues of interest to its membership. Members include engineers, scientists, and mathematicians, both those employed in academia and those working in industry. The society supports educational institutions promoting applied mathematics.
Joseph Hillel Silverman is a professor of mathematics at Brown University working in arithmetic geometry, arithmetic dynamics, and cryptography.
Objective-collapse theories, also known as models of spontaneous wave function collapse or dynamical reduction models, are proposed solutions to the measurement problem in quantum mechanics. As with other theories called interpretations of quantum mechanics, they are possible explanations of why and how quantum measurements always give definite outcomes, not a superposition of them as predicted by the Schrödinger equation, and more generally how the classical world emerges from quantum theory. The fundamental idea is that the unitary evolution of the wave function describing the state of a quantum system is approximate. It works well for microscopic systems, but progressively loses its validity when the mass / complexity of the system increases.
Cliodynamics is a transdisciplinary area of research that integrates cultural evolution, economic history/cliometrics, macrosociology, the mathematical modeling of historical processes during the longue durée, and the construction and analysis of historical databases.
Celestial Mechanics and Dynamical Astronomy is a scientific journal covering the fields of astronomy and astrophysics. It was established as Celestial Mechanics in June 1969. The journal is published by Springer Science+Business Media and the editor-in-chief is Alessandra Celletti, while Sylvio Ferraz-Mello is honorary editor.
Victor Vladimirovich Goryunov is a Russian mathematician born in 1956. He is a leading figure in Singularity theory, whose contributions to the subject are fundamental. He has published several books and a variety of papers in singularity theory, finite type invariants, and Legendrian knots. Many of his papers in Lagrangian and Legendrian geometry are now considered to be classical in the subject.
Nonlinear Dynamics, An International Journal of Nonlinear Dynamics and Chaos in Engineering Systems is a monthly peer-reviewed scientific journal covering all nonlinear dynamic phenomena associated with mechanical, structural, civil, aeronautical, ocean, electrical, and control systems. It is published by Springer Nature and the editor-in-chief of the journal is Walter Lacarbonara.
Communications in Contemporary Mathematics (CCM) is a journal published by World Scientific since 1999. It covers research in the fields such as applied mathematics, dynamical systems, mathematical physics, and topology.
Groups, Geometry, and Dynamics is a quarterly peer-reviewed mathematics journal published quarterly by the European Mathematical Society. It was established in 2007 and covers all aspects of groups, group actions, geometry and dynamical systems. The journal is indexed by Mathematical Reviews and Zentralblatt MATH. Its 2009 MCQ was 0.65, and its 2012 impact factor is 0.867.
Mathematics is a field of study that investigates topics such as number, space, structure, and change.
Joseph Pierre LaSalle was an American mathematician specialising in dynamical systems and responsible for important contributions to stability theory, such as LaSalle's invariance principle which bears his name.
Jack Kenneth Hale was an American mathematician working primarily in the field of dynamical systems and functional differential equations.
Robert Luke Devaney is an American mathematician, the Feld Family Professor of Teaching Excellence at Boston University. His research involves dynamical systems and fractals.
The Journal of Modern Dynamics is a peer-reviewed scientific journal of mathematics published by the American Institute of Mathematical Sciences with the support of the Anatole Katok Center for Dynamical Systems and Geometry. The editor-in-chief is Giovanni Forni.
