Functions that are universal with respect to the trigonometric system

Martin Gevorgovich Grigoryan; Levon Nikolaevich Galoyan

doi:10.1070/im8964

Functions that are universal with respect to the trigonometric system

Izvestiya Mathematics ◽

10.1070/im8964 ◽

2021 ◽

Vol 85 (2) ◽

Author(s):

Martin Gevorgovich Grigoryan ◽

Levon Nikolaevich Galoyan

Keyword(s):

Trigonometric System

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Convergence of greedy approximation for the trigonometric system

Analysis Mathematica ◽

10.1007/s10476-005-0007-0 ◽

2005 ◽

Vol 31 (2) ◽

pp. 85-115 ◽

Cited By ~ 2

Author(s):

S. V. Konyagin ◽

V. N. Temlyakov

Keyword(s):

Trigonometric System ◽

Greedy Approximation

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On Parseval’s equality for rearrangements of the trigonometric system

Mathematical Notes ◽

10.1134/s0001434611110186 ◽

2011 ◽

Vol 90 (5-6) ◽

pp. 780-783

Author(s):

A. I. Rubinshtein

Keyword(s):

Trigonometric System ◽

Parseval’S Equality

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Analysis of chaotic characteristics of trigonometric function system

Modern Physics Letters B ◽

10.1142/s0217984920502103 ◽

2020 ◽

Vol 34 (21) ◽

pp. 2050210

Author(s):

Wanbo Yu ◽

Ting Yu

Keyword(s):

Social Sciences ◽

Dynamic System ◽

Necessary Conditions ◽

Fluid Motion ◽

Nonlinear Dynamic System ◽

Chaotic Sequence ◽

Trigonometric System ◽

Secure Communications ◽

Key Space ◽

Mathematical Derivation

Chaos, as an important subject of nonlinear science, plays an important role in solving problems in both natural sciences and social sciences such as the fields of secure communications, fluid motion, particle motion and so on. Aiming at this problem, this paper proposes a nonlinear dynamic system composed of product trigonometric functions and studies its chaotic characteristics. Through the mathematical derivation of the system’s period, the analysis of the necessary conditions at the fixed point, the experimental drawing of the Lyapunov exponential graph and the branch graph of the system, it is proved that the system has larger chaotic interval and stronger chaotic characteristics. The parameters of the proposed dynamic system are generated randomly, and then the chaotic sequence can be generated. The chaotic sequence is used to encrypt the digital image, a good encryption effect is obtained, and there is a large key space. At the same time, the motion of the particles in the space magnetic field is simulated, which further proves that the trigonometric system has strong chaotic characteristics.

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