Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
1. Prove that map R₁ ×R¹ → R¹ given by (t, x) → x(t²+1) is not a dynamical system on R. Prove that map R₁ × R² → R² given by (t, x) → - sint cos t cos t sin t is a dynamical system on R2. Hint: one easy way is to recall the geometric meaning of this X, X = X1 X2 2

1. Prove that map R₁ ×R¹ → R¹ given by (t, x) → x(t²+1) is not a dynamical system on R. Prove that map R₁ × R² → R² given by (t, x) → - sint cos t cos t sin t is a dynamical system on R2. Hint: one easy way is to recall the geometric meaning of this X, X = X1 X2 2

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
1. Prove that map R₁×R¹ → R¹ given by (t, x) → x(t²+1) is not a dynamical system on R. Prove that map R₁ × R² → R² given by (t, x) → is a dynamical system on R2. Hint: one easy way is to recall the geometric meaning of this matrix transformation. Another approach is to use the complex numbers and relate to eit (x1 + ix2). For the latter dynamical system o fix any SC R². Draw (S). cos t sin t sin cos t X, X = X1 x2 2
Transcribed Image Text:1. Prove that map R₁×R¹ → R¹ given by (t, x) → x(t²+1) is not a dynamical system on R. Prove that map R₁ × R² → R² given by (t, x) → is a dynamical system on R2. Hint: one easy way is to recall the geometric meaning of this matrix transformation. Another approach is to use the complex numbers and relate to eit (x1 + ix2). For the latter dynamical system o fix any SC R². Draw (S). cos t sin t sin cos t X, X = X1 x2 2
Expert Solution
steps

Step by step

Solved in 4 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS