Nonlinear Dynamics and Chaotic Phenomena: An Introduction
Home > Technology & Engineering > Mechanical engineering & materials > Mechanical engineering > Tribology (friction & lubrication) > Nonlinear Dynamics and Chaotic Phenomena: An Introduction
Nonlinear Dynamics and Chaotic Phenomena: An Introduction

Nonlinear Dynamics and Chaotic Phenomena: An Introduction


     0     
5
4
3
2
1



International Edition


About the Book

1 Nonlinear Ordinary Differential Equations.- 1.1 First-order Systems.- 1.1.1 Dynamical System.- 1.1.2 Lipschitz Condition.- 1.1.3 Gronwall's Lemma.- 1.1.4 Linear Equations.- 1.1.5 Autonomous Equations.- 1.1.6 Stability of Equilibrium Points.- 1.1.6.1 Liapunov and Asymptotic Stability.- 1.1.6.2 Liapunov Function Method.- 1.1.7 Center Manifold Theorem.- 1.2 Phase-plane Analysis.- 1.3 Fully Nonlinear Evolution.- 1.4 Non-autonomous Systems.- 2 Bifurcation Theory.- 2.1 Stability and Bifurcation.- 2.2 Saddle-Node, Transcritical and Pitchfork Bifurcations.- 2.3 Hopf Bifurcation.- 2.4 Break-up of Bifurcations under Perturbations.- 2.5 Bifurcation Theory of One-Dimensional Maps.- 2.6 Appendix: The Normal Form Reduction.- 3 Hamiltonian Dynamics.- 3.1 Hamilton's Equations.- 3.2 Phase Space.- 3.3 Canonical Transformations.- 3.4 The Hamilton-Jacobi Equation.- 3.5 Action-Angle Variables.- 3.6 Infinitesimal Canonical Transformations.- 3.7 Poisson's Brackets.- 4 Integrable Systems.- 4.1 Separable Hamiltonian Systems.- 4.2 Integrable Systems.- 4.3 Dynamics on the Tori.- 4.4 Canonical Perturbation Theory.- 4.5 Komogorov-Arnol'd-Moser Theory.- 4.6 Breakdown of Integrability and Criteria for Transition to Chaos.- 4.6.1 Local Criteria.- 4.6.2 Local Stability vs. Global Stability.- 4.6.3 Global Criteria.- 4.7 Magnetic Island Overlap and Stochasticity in Magnetic Confinement Systems.- 4.8 Appendix: The Problem of Internal Resonance in Nonlinearly-Coupled Systems.- 5 Chaos in Conservative Systems.- 5.1 Phasse-Space Dynamics of Conservative Systems.- 5.2 Poincar´e's Surface of Section.- 5.3 Area-preserving Mappings.- 5.4 Twist Maps.- 5.5 Tangent Maps.- 5.6 Poincar´e-Birkhoff Fixed-Point Theorem.- 5.7 Homoclinic and Heteroclinic Points.- 5.8 Quantitative Measures of Chaos.- 5.8.1 Liapunov Exponents.- 5.8.2 Kolmogorov Entropy.- 5.8.3 Autocorrelation Function.- 5.8.4 Power Spectra.- 5.9 Ergodicity and Mixing.- 5.9.1 Ergodicity.- 5.9.2 Mixing.- 5.9.3 Baker's Tranformation.- 5.9.4 Lagrangian Chaos in Fluids.- 6 Chaos in Dissipative Systems.- 6.1 Phase-Space Dynamics of Dissipative Systems.- 6.2 Strange Attractors.- 6.3 Fractals.- 6.3.1 Examples of Fractals.- 6.3.2 Box-Counting Method.- 6.4 Multi-fractals.- 6.5 Analysis of Time Series Data.- 6.6 The Lorenz Attractor.- 6.6.1 Equilibrium Solutions and Their Stability.- 6.6.2 Slightly Supercritical Case.- 6.6.3 Existence of an Attractor .- 6.6.4 Chaotic Behavior of the Nonlinear Solutions.- 6.7 Period-Doubling Bifurcations.- 6.7.1 Difference Equations.- 6.7.2 The Logistic Map.- 6.8 Appendix: The Hausdorff-Besicovitch Dimension.- 6.9 Appendix: The Derivation of Lorenz's Equations.- 6.10 Appendix: The Derivation of Universality for One-Dimensional Maps.- 7 Solitons.- 7.1 Fermi-Pasta-Ulam Recurrence.- 7.2 Korteweg-deVries Equation.- 7.3 Waves in an Anharmonic Lattice.- 7.4 Shallow Water Waves.- 7.5 Ion-acoustic Waves.- 7.6 Basic Properties of Korteweg-deVries Equation.- 7.6.1 Effect of Nonlinearity.- 7.6.2 Effect of Dispersion.- 7.6.3 Similarity Transformation.- 7.6.4 Stokes Waves: Periodic Solutions.- 7.6.5 Solitary Waves.- 7.6.6 Peridic Cnoidal Wave Solutions.- 7.6.7 Interacting Solitary Waves: Hirota's Method.- 7.7 Inverse-Scattering Transform Method.- 7.7.1 Time Evolution of the Scattering Data.- 7.7.2 Gel'fand-Levitan-Marchenko Equation.- 7.7.3 Direct Scattering Problem.- 7.7.4 Inverse-Scattering Problem.- 7.8 Conservation Laws.- 7.9 Lax Formulation.- 7.10 B]acklund Transformations.- 8 Singularity Analysis and the Painlev´e Property of Dynamical Systems.- 8.1 The Painlev´e Property.- 8.2 Singularity Analysis.- 8.3 The Painlev´e Property for Partial Differential Equations.- 9 Fractals and Multi-Fractals in Turbulence.- 9.1 Scale Invariance of the Navier-Stokes Equations and the Kolmogorov (1941) Theory.- 9.2 The β -model for Turbulence.- 9.3 The Multi-fractal Models.- 9.4 The Random-β Model.- 9.5 The Transition to Dissipation Range.- 9.6 Critical Phenomena Perspectives on the Turbulence P


Best Sellers



Product Details
  • ISBN-13: 9789401777117
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Edition: 0002-Softcover Repri
  • Language: English
  • Returnable: N
  • Spine Width: 21 mm
  • Width: 156 mm
  • ISBN-10: 940177711X
  • Publisher Date: 27 Sep 2016
  • Binding: Paperback
  • Height: 234 mm
  • No of Pages: 375
  • Series Title: Fluid Mechanics and Its Applications
  • Weight: 616 gr


Similar Products

Add Photo
Add Photo

Customer Reviews

REVIEWS      0     
Click Here To Be The First to Review this Product
Nonlinear Dynamics and Chaotic Phenomena: An Introduction
Springer -
Nonlinear Dynamics and Chaotic Phenomena: An Introduction
Writing guidlines
We want to publish your review, so please:
  • keep your review on the product. Review's that defame author's character will be rejected.
  • Keep your review focused on the product.
  • Avoid writing about customer service. contact us instead if you have issue requiring immediate attention.
  • Refrain from mentioning competitors or the specific price you paid for the product.
  • Do not include any personally identifiable information, such as full names.

Nonlinear Dynamics and Chaotic Phenomena: An Introduction

Required fields are marked with *

Review Title*
Review
    Add Photo Add up to 6 photos
    Would you recommend this product to a friend?
    Tag this Book Read more
    Does your review contain spoilers?
    What type of reader best describes you?
    I agree to the terms & conditions
    You may receive emails regarding this submission. Any emails will include the ability to opt-out of future communications.

    CUSTOMER RATINGS AND REVIEWS AND QUESTIONS AND ANSWERS TERMS OF USE

    These Terms of Use govern your conduct associated with the Customer Ratings and Reviews and/or Questions and Answers service offered by Bookswagon (the "CRR Service").


    By submitting any content to Bookswagon, you guarantee that:
    • You are the sole author and owner of the intellectual property rights in the content;
    • All "moral rights" that you may have in such content have been voluntarily waived by you;
    • All content that you post is accurate;
    • You are at least 13 years old;
    • Use of the content you supply does not violate these Terms of Use and will not cause injury to any person or entity.
    You further agree that you may not submit any content:
    • That is known by you to be false, inaccurate or misleading;
    • That infringes any third party's copyright, patent, trademark, trade secret or other proprietary rights or rights of publicity or privacy;
    • That violates any law, statute, ordinance or regulation (including, but not limited to, those governing, consumer protection, unfair competition, anti-discrimination or false advertising);
    • That is, or may reasonably be considered to be, defamatory, libelous, hateful, racially or religiously biased or offensive, unlawfully threatening or unlawfully harassing to any individual, partnership or corporation;
    • For which you were compensated or granted any consideration by any unapproved third party;
    • That includes any information that references other websites, addresses, email addresses, contact information or phone numbers;
    • That contains any computer viruses, worms or other potentially damaging computer programs or files.
    You agree to indemnify and hold Bookswagon (and its officers, directors, agents, subsidiaries, joint ventures, employees and third-party service providers, including but not limited to Bazaarvoice, Inc.), harmless from all claims, demands, and damages (actual and consequential) of every kind and nature, known and unknown including reasonable attorneys' fees, arising out of a breach of your representations and warranties set forth above, or your violation of any law or the rights of a third party.


    For any content that you submit, you grant Bookswagon a perpetual, irrevocable, royalty-free, transferable right and license to use, copy, modify, delete in its entirety, adapt, publish, translate, create derivative works from and/or sell, transfer, and/or distribute such content and/or incorporate such content into any form, medium or technology throughout the world without compensation to you. Additionally,  Bookswagon may transfer or share any personal information that you submit with its third-party service providers, including but not limited to Bazaarvoice, Inc. in accordance with  Privacy Policy


    All content that you submit may be used at Bookswagon's sole discretion. Bookswagon reserves the right to change, condense, withhold publication, remove or delete any content on Bookswagon's website that Bookswagon deems, in its sole discretion, to violate the content guidelines or any other provision of these Terms of Use.  Bookswagon does not guarantee that you will have any recourse through Bookswagon to edit or delete any content you have submitted. Ratings and written comments are generally posted within two to four business days. However, Bookswagon reserves the right to remove or to refuse to post any submission to the extent authorized by law. You acknowledge that you, not Bookswagon, are responsible for the contents of your submission. None of the content that you submit shall be subject to any obligation of confidence on the part of Bookswagon, its agents, subsidiaries, affiliates, partners or third party service providers (including but not limited to Bazaarvoice, Inc.)and their respective directors, officers and employees.

    Accept

    New Arrivals



    Inspired by your browsing history


    Your review has been submitted!

    You've already reviewed this product!