scholarly journals On fixed points of dynamical systems

1990 ◽  
Vol 110 (1) ◽  
pp. 263-263 ◽  
Author(s):  
Cem Tezer
Keyword(s):  
Dynamical Systems ◽  
Fixed Points

scholarly journals LEARNING TRAJECTORIES OF DYNAMICAL SYSTEMS

2012 ◽  
Vol 17 (4) ◽  
pp. 519-531
Author(s):  
Helle Hein ◽  
Ulo Lepik
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Fixed Points ◽  
Error Function ◽  
Numerical Results ◽  
Learning Trajectories ◽  
Periodic Trajectories

The aim of the present paper is to describe the method that is capable of adjusting the parameters of a dynamical system so that the trajectories gain certain specified properties. Three problems are considered: (i) learning fixed points, (ii) learning to periodic trajectories, (iii) restrictions on the trajectories. An error function, which measures the discrepancy between the actual and desired trajectories is introduced. Numerical results of several examples, which illustrate the efficiency of the method, are presented.

scholarly journals Fixed Points, Symmetries, and Bounds for Basins of Attraction of Complex Trigonometric Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Kasey Bray ◽  
Jerry Dwyer ◽  
Roger W. Barnard ◽  
G. Brock Williams
Keyword(s):  
Dynamical Systems ◽  
Fixed Points ◽  
Basins Of Attraction ◽  
Trigonometric Functions ◽  
Fractal Image ◽  
Fractal Images

The dynamical systems of trigonometric functions are explored, with a focus on tz=tanz and the fractal image created by iterating the Newton map, Ftz, of  tz. The basins of attraction created from iterating  Ftz are analyzed, and some bounds are determined for the primary basins of attraction. We further prove x- and y-axis symmetry of the Newton map and explore the nature of the fractal images.

scholarly journals Fixed Points and Fermat: A Dynamical Systems Approach to Number Theory

2000 ◽  
Vol 107 (5) ◽  
pp. 422-428
Author(s):  
Michael Frame ◽  
Brenda Johnson ◽  
Jim Sauerberg
Keyword(s):  
Number Theory ◽  
Dynamical Systems ◽  
Fixed Points ◽  
Systems Approach
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