• Journal of the Korean Mathematical Society
• /
• v.61 no.1
• /
• pp.1-28
• /
• 2024

In this article, we associate a contact structure to the conjugacy class of a periodic surface homeomorphism, encoded by a combinatorial tuple of integers called a marked data set. In particular, we prove that infinite families of these data sets give rise to Stein fillable contact structures with associated monodromies that do not factor into products to positive Dehn twists. In addition to the above, we give explicit constructions of symplectic fillings for rational open books analogous to Mori's construction for honest open books. We also prove a sufficient condition for the Stein fillability of rational open books analogous to the positivity of monodromy for honest open books due to Giroux and Loi-Piergallini.

• Communications of the Korean Mathematical Society
• /
• v.34 no.3
• /
• pp.967-979
• /
• 2019

Chaotic dynamical systems, preferably on a Cantor-like space with some arithmetic operations are considered as good pseudo-random number generators. There are many definitions of chaos, of which Devaney-chaos and pos itive topological entropy seem to be the strongest. Let $A=\{0,1,{\dots},p-1\}$. We define a continuous map on $A^{\mathbb{Z}}$ using addition with a carry, in combination with the shift map. We show that this map gives rise to a dynamical system with positive entropy, which is also Devaney-chaotic: i.e., it is transitive, sensitive and has a dense set of periodic points.

• Journal of the Chungcheong Mathematical Society
• /
• v.13 no.1
• /
• pp.101-107
• /
• 2000

For a continuous map f of the circle to itself, we show that if P(f) is closed, then ${\Gamma}(f)$ is closed, and ${\Omega}(f)={\Omega}(f^n)$ for all n > 0.

• The Journal of Natural Sciences
• /
• v.14 no.1
• /
• pp.1-6
• /
• 2004

In this paper, we calculate the Nielsen numbers of periods for maps on the Klein bottle.

• Communications of the Korean Mathematical Society
• /
• v.15 no.3
• /
• pp.549-553
• /
• 2000

For a continuous map of the circle to itself, we give necessary and sufficient conditions for the $\omega$-limit set of each nonwandering point to be minimal.

• Bulletin of the Korean Mathematical Society
• /
• v.36 no.1
• /
• pp.147-159
• /
• 1999

Tabanov investigated the global symmetric perturbation of the integrable billiard mapping in the ellipse [3]. He showed the nonintegrability of the Birkhoff billiard in the perturbed domain by proving that the principal separatrices splitting angle is not zero.In this paper, using the exact separatrix map of an one-degree-of freedom Hamiltoniam system with time periodic perturbation, we show the existence the stochastic layer including the uniformly hyperbolic invariant set which implies the nonintegrability near the separatrices of a Birkhoff's billiard in the domain bounded by $C^2$ convex simple curve constructed by the generic global perturbation of the ellipse.

• Journal of Mechanical Science and Technology
• /
• v.17 no.12
• /
• pp.1922-1927
• /
• 2003

Nonlinear normal mode (NNM) vibration, in a nonlinear dual mass Hamiltonian system, which has 6$\^$th/ order homogeneous polynomial as a nonlinear term, is studied in this paper. The existence, bifurcation, and the orbital stability of periodic motions are to be studied in the phase space. In order to find the analytic expression of the invariant curves in the Poincare Map, which is a mapping of a phase trajectory onto 2 dimensional surface in 4 dimensional phase space, Whittaker's Adelphic Integral, instead of the direct integration of the equations of motion or the Birkhoff-Gustavson (B-G) canonical transformation, is derived for small value of energy. It is revealed that the integral of motion by Adelphic Integral is essentially consistent with the one obtained from the B-G transformation method. The resulting expression of the invariant curves can be used for analyzing the behavior of NNM vibration in the Poincare Map.

• Journal of applied mathematics & informatics
• /
• v.14 no.1_2
• /
• pp.277-288
• /
• 2004

In this paper, we discuss a continuous self-map of an interval and the existence of an uncountable strongly chaotic set. It is proved that if a continuous self-map of an interval has positive topological entropy, then it has an uncountable strongly chaotic set in which each point is recurrent, but is not almost periodic.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.38A no.8
• /
• pp.629-637
• /
• 2013

Chaos communication systems have the characteristics such as non-periodic, wide-band, non-predictability of signals and easy implementation. There have been many studies about chaos communication systems because of these advantages. But, chaos communication systems have low BER(Bit Error Rate) compare to general digital communication system. Existing researches on chaos communication systems only analyze BER performance according to various chaos maps. There are no studies on analysis of BER performance according to PDF(Probability Density Function) of chaos maps. In this paper, we analyze the BER performance according to changing parameter, equation, and initial values of chaos map's PDF. In addition, we propose new chaos map to improve BER performance. Simulation results show that BER performance of CDSK(Correlation Delay Shift Keying) is changed when PDF of chaos map changed. And the proposed chaos map has a better BER performance compare to previous chaos maps such as Tent map, Logistic map, and Henon map.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 1996.04a
• /
• pp.177-183
• /
• 1996

By utilizing the concept of normal modes, nonlinear dynamics is studied on pendulum dynamic absorber. When the spring mode loses the stability in undamped free system, a dynamic two-well potential is formed in Poincare map. A procedure is formulated to compute the forced responses associated with bifurcating mode and predict double saddle-loop phenomenon. It is found that quasiperiodic motion and stable periodic motion coexist in some parameter ranges, and only periodic motions or rotation of pendulum with chaotic fluctuation are observed in other ranges.