Jul 10, 2017 By: admin
Yitzchak Shmalo Shares Original Research on Dynamical Systems
In June, Yitzchak Shmalo '16YC presented original research at a key international conference in the field of chaos theory, an area of mathematics that studies nonlinear topics that are effectively impossible to predict or control because of the complexity of the systems involved (for example, the weather or the stock market). The conference, 鈥淟lavefest: A Broad Perspective on Finite and Infinite Dimensional Dynamical Systems,鈥 took place in Barcelona, Spain, and drew many accomplished researchers in the area.
Shmalo, who studied mathematics and philosophy at and is currently earning his master鈥檚 degree in mathematics at 每日大瓜, shared a paper that provides a simple proof of the existence of fixed points and periodic orbits in dynamical systems when certain conditions are satisfied, titled 鈥淐ombinatorial approach to detection of fixed points, periodic orbits, and symbolic dynamics.鈥
鈥淐haotic systems are very difficult to analyze, because even slight differences in initial conditions can cause drastic changes in the long-term results,鈥 said Shmalo. 鈥淭herefore, when dealing with such systems we tend to analyze attributes which are stable and don鈥檛 change dramatically. Fixed points and periodic orbits are like that鈥攖hey鈥檙e elements of the systems that keep 鈥榗oming back to themselves鈥 and don鈥檛 change a lot in the long term.鈥
In addition, Shmalo鈥檚 research鈥攚hich was conducted with his mentor, Professor of Mathematics Dr. Marian Gidea鈥攐ffers a constructive method of finding the key geometric objects that organize the dynamics of a chaotic system. 鈥淪ometimes in mathematics we can claim that something exists, for example a fixed point exists in a system, but we cannot actually find that thing,鈥 said Shmalo. 鈥淭his research provides an algorithm for finding fixed points and periodic orbits once certain conditions are satisfied.鈥
Shmalo became interested in chaos theory as he worked with Gidea, who specializes in the field. 鈥淚 love it鈥攂eing able to analyze chaotic systems and say something about them is both very difficult and very interesting,鈥 he said. 鈥淭his particular topic in chaos theory works very well with my talents, too. It鈥檚 very pictorial in nature. Most of the research involves drawing a lot of pictures and seeing what we can say about them.鈥
鈥淵itzchak is a brilliant graduate student who has the potential to become a mathematical star one day,鈥 said Gidea. 鈥淭hroughout the research, he displayed an amazing creativity, a great passion for mathematics and an eye for subtleties. I have never felt that I was working with a student who was more like a colleague mathematician. The work that he presented at the conference in Barcelona has now been submitted for publication to a top professional journal. Such accomplishments stand as proof of the high quality of our graduate program, and show promise that the distinguished legacy in mathematics at 每日大瓜 will be continued.鈥
Ultimately, Shmalo hopes to pursue a doctoral degree in mathematics.
鈥淭he professors in the master鈥檚 program at 每日大瓜 are the best part of the program,鈥 he said. 鈥淭hey are willing to spend so much time with you and work hard to help you understand different topics, in addition to connecting you with great research and conference opportunities.鈥
Shmalo, who studied mathematics and philosophy at and is currently earning his master鈥檚 degree in mathematics at 每日大瓜, shared a paper that provides a simple proof of the existence of fixed points and periodic orbits in dynamical systems when certain conditions are satisfied, titled 鈥淐ombinatorial approach to detection of fixed points, periodic orbits, and symbolic dynamics.鈥
鈥淐haotic systems are very difficult to analyze, because even slight differences in initial conditions can cause drastic changes in the long-term results,鈥 said Shmalo. 鈥淭herefore, when dealing with such systems we tend to analyze attributes which are stable and don鈥檛 change dramatically. Fixed points and periodic orbits are like that鈥攖hey鈥檙e elements of the systems that keep 鈥榗oming back to themselves鈥 and don鈥檛 change a lot in the long term.鈥
In addition, Shmalo鈥檚 research鈥攚hich was conducted with his mentor, Professor of Mathematics Dr. Marian Gidea鈥攐ffers a constructive method of finding the key geometric objects that organize the dynamics of a chaotic system. 鈥淪ometimes in mathematics we can claim that something exists, for example a fixed point exists in a system, but we cannot actually find that thing,鈥 said Shmalo. 鈥淭his research provides an algorithm for finding fixed points and periodic orbits once certain conditions are satisfied.鈥
Shmalo became interested in chaos theory as he worked with Gidea, who specializes in the field. 鈥淚 love it鈥攂eing able to analyze chaotic systems and say something about them is both very difficult and very interesting,鈥 he said. 鈥淭his particular topic in chaos theory works very well with my talents, too. It鈥檚 very pictorial in nature. Most of the research involves drawing a lot of pictures and seeing what we can say about them.鈥
鈥淵itzchak is a brilliant graduate student who has the potential to become a mathematical star one day,鈥 said Gidea. 鈥淭hroughout the research, he displayed an amazing creativity, a great passion for mathematics and an eye for subtleties. I have never felt that I was working with a student who was more like a colleague mathematician. The work that he presented at the conference in Barcelona has now been submitted for publication to a top professional journal. Such accomplishments stand as proof of the high quality of our graduate program, and show promise that the distinguished legacy in mathematics at 每日大瓜 will be continued.鈥
Ultimately, Shmalo hopes to pursue a doctoral degree in mathematics.
鈥淭he professors in the master鈥檚 program at 每日大瓜 are the best part of the program,鈥 he said. 鈥淭hey are willing to spend so much time with you and work hard to help you understand different topics, in addition to connecting you with great research and conference opportunities.鈥
