This book stems from lectures that were delivered at the three-week Advanced Instructional School on Ergodic Theory and Dynamical Systems held at the Indian Institute of Technology Delhi, from 4-23 December 2017, with the support of the National Centre for Mathematics, National Board for Higher Mathematics, Department of Atomic Energy, Government of India. The book discusses various aspects of dynamical systems. Each chapter of this book specializes in one aspect of dynamical systems and thus begins at an elementary level and goes on to cover fairly advanced material. The book helps researchers be familiar with and navigate through different parts of ergodic theory and dynamical systems.

Autorentext

ANIMA NAGAR is Associate Professor at the Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, India. She completed her doctoral studies at Gujarat University in 1999 and spent her postdoctoral years at the University of Hyderabad, India. She has mainly held visiting positions at the University of Maryland, USA, and Technical University Wein as well as the University of Wein, Austria. Her research interests are in topological dynamics and symbolic dynamics.

RIDDHI SHAH is Professor of Mathematics at the School of Physical Sciences, Jawaharlal Nehru University, New Delhi, India, since 2007. Earlier, she was a faculty at the School of Mathematics, Tata Institute of Fundamental Research (TIFR), Mumbai, India from 1990 to 2007. She has held visiting positions at several universities in France, Germany, Israel, Japan and the USA; some of these were supported by the Alexander von Humboldt fellowship, CNRS research fellowship and the Japan Society for the Promotion of Science (JSPS) invitation fellowship. She worked for her Ph.D. at TIFR, Mumbai, India, and was awarded the Young Scientist Medal from the Indian National Science Academy (INSA) in 1995.

Currently, Prof. Shah is Member of the National Board for Higher Mathematics (NBHM) and also Member of the executive committee of the Indian Women and Mathematics (IWM) and served as its Chair from 2016 to 2019. Her biographical essay featured in Lilavati's Daughters, a publication of the Indian Academy of Sciences on women scientists of India. She has published many research articles in respected international journals and has coedited a book on Recent Trends in Ergodic Theory and Dynamical Systems. Her research interests include probabilities on groups, dynamics of group actions and the structure of groups.

SHRIHARI SRIDHARAN is Associate Professor at the School of Mathematics, Indian Institute of Science Education and Research Thiruvananthapuram (IISER-TVM), India, since 2014. Earlier, he was Faculty at the Chennai Mathematical Institute (CMI), India, and the Indian Institute of Technology Guwahati (IIT-G), India. He has held a visiting position at the Institute of Mathematics, Polish Academy of Sciences (IM-PAN). He obtained his Ph.D. from the University of Manchester, UK, in 2004, and has held post­doctoral positions at the Institute of Mathematical Sciences (IMSc), Chennai, India, and the Indian Institute of Science (IISc), Bengaluru, India.

Sridharan's research interests focus mainly on holomorphic, non-invertible dynamical systems on the Riemann sphere. He has contributed towards various aspects in finer analysis of Julia sets of polynomials as well as rational functions, working on both open and closed dynamics. He also works on systems of holomorphic correspondences, correspondences generated by a finite rational semigroup and ergodic theory.

Inhalt

V. Kannan: Real Dynamics.- Anima Nagar and C. R. E. Raja: Topological Dynamics.- C. S. Aravinda and Vishesh S. Bhat: Basic Ergodic Theory.- Siddhartha Bhattacharya: Symbolic Dynamics.- Shrihari Sridharan and Kaushal Verma: Complex Dynamics.- Anish Ghosh: Topics in Homogeneous Dynamics and Number Theory.- S. G. Dani: On Certain Unusual Large Subsets Arising as Winning Sets of Some Games.