Anatole Katok facts for kids
Quick facts for kids
Anatole Katok
|
|
|---|---|
| Анатолий Борисович Каток | |
 |
|
| Born | August 9, 1944 Washington, D.C., U.S.
|
| Died | April 30, 2018 (aged 73) Danville, Pennsylvania, U.S.
|
| Alma mater | Moscow State University |
| Known for | Important contributions to ergodic theory and dynamical systems |
| Scientific career | |
| Fields | Mathematics – dynamical systems |
| Institutions | |
| Doctoral advisor | Yakov Sinai |
Anatoly Borisovich Katok (Russian: Анатолий Борисович Каток; born August 9, 1944 – died April 30, 2018) was an American mathematician. He was born in the U.S. but had Russian-Jewish family roots.
Katok was a leader at the Center for Dynamics and Geometry at Pennsylvania State University. His main area of study was the theory of dynamical systems. This field looks at how systems change over time. Think of how planets move or how weather patterns develop.
Contents
Early Life and Education
Anatole Katok studied at Moscow State University in Russia. He earned his master's degree in 1965. Then, in 1968, he completed his PhD. His PhD work was about using special math methods to understand how systems change. His teacher was a famous mathematician named Yakov Sinai.
In 1978, Katok moved to the United States. He was married to Svetlana Katok, who is also a mathematician. She also studies dynamical systems. They worked together on a special program for college students at Penn State.
Amazing Math Work
When Anatole Katok was a student, he worked with A. Stepin. They created a special math idea called "Katok-Stepin approximations." This idea helped solve some old math problems. These problems were first thought about by famous mathematicians like John von Neumann and Andrey Kolmogorov. Katok and Stepin won a prize from the Moscow Mathematical Society in 1967 for their work.
Katok also developed other important math ideas. One of these was about how to change the "time" in a system. He also found ways to build special math structures. For example, he created examples of systems that behave in a very unpredictable way.
He worked with other mathematicians like Elon Lindenstrauss and Manfred Einsiedler. Together, they made big steps in solving a math problem called the Littlewood conjecture. This problem is about how well numbers can be approximated by fractions.
Anatole Katok was also known for creating new math problems and challenges. He even offered prizes for solving them! One of his most famous ideas is the Katok Entropy Conjecture. This idea connects the shape of a system to how it changes over time. It was one of the first ideas to show how "rigid" some dynamical systems are. In his later years, Katok studied other types of "rigidity" in math. He worked with many colleagues on these complex ideas.
Katok also studied how unpredictable systems behave. He looked at things like how often a system returns to a similar state. He gave important talks about his work at big math conferences. For example, he spoke at the International Congress of Mathematicians in 1983.
Katok wrote a very important book with his former student, Boris Hasselblatt. It's called Introduction to the Modern Theory of Dynamical Systems. This book came out in 1995. Many people consider it a key book for understanding modern dynamical systems. It is one of the most referenced books in this area of math.
Anatole Katok was the main editor for the Journal of Modern Dynamics. He also helped edit many other important math publications.
Teaching and Mentoring
Katok taught at several universities during his career. He was a professor at the University of Maryland from 1978 to 1984. Then he moved to the California Institute of Technology from 1984 to 1990. Since 1990, he taught at Pennsylvania State University. There, he held a special professorship called the Raymond N. Shibley professorship.
He was a great teacher and mentor. He guided 44 students as they worked on their PhDs. Many of his students and their students have gone on to become mathematicians themselves.
Awards and Recognition
Anatole Katok received many honors for his work.
- In 1967, he won the Moscow Mathematical Society for Young Mathematicians Prize. He shared this award with A. Stepin and V. Oseledets.
- In 1983, he was invited to speak at the International Congress of Mathematicians in Warsaw. This is a very important event for mathematicians.
- In 2004, he became a member of the American Academy of Arts and Sciences.
- In 2012, he was named a fellow of the American Mathematical Society. This is a high honor for mathematicians in the U.S.
Selected Books
Anatole Katok wrote or edited several important books about dynamical systems:
- Anatole Katok and Boris Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, 1995.
- Boris Hasselblatt and Anatole Katok, A First Course in Dynamics with a Panorama of Recent Developments, Cambridge University Press, 2003.
- Anatole Katok, Combinatorial Constructions in Ergodic Theory and Dynamics, Pennsylvania State University, 2003.
- Anatole Katok and Boris Hasselblatt (eds.), Handbook of Dynamical Systems Vol 1A, Elsevier 2002.
- Anatole Katok and Boris Hasselblatt (eds.), Handbook of Dynamical Systems, Vol 1B, Elsevier 2005.
- Anatole Katok and Vaughn Climenhaga, Lectures on Surfaces: (Almost) Everything You Wanted to Know about Them, Pennsylvania State University – AMS, 2008.
- Anatole Katok and Viorel Nitica, Rigidity in Higher Rank Abelian Group Actions: Volume 1, Cambridge University Press, June 2011.
