Lecture Notes on Dynamical Systems, Chaos And Fractal Geometry
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Lecture Notes on Dynamical Systems, Chaos And Fractal Geometry
Lecture Notes on Dynamical Systems, Chaos And Fractal Geometry
Topics covered in
this notes include: The Orbits of One-Dimensional Maps, Bifurcation and the
Logistic Family, Sharkovsky’s Theorem, Metric Spaces, Devaney’s Definition
of Chaos, Conjugacy of Dynamical Systems, Singer’s Theorem, Fractals,
Newton’s Method, Iteration of Continuous Functions, Linear Transformation
and Transformations Induced by Linear Transformations, Some Elementary
Complex Dynamics, Examples of Substitutions, Compactness in Metric Spaces
and the Metric Properties of Substitutions, Substitution Dynamical Systems,
Sturmian Sequences and Irrational Rotations.
Author(s): Geoffrey
R. Goodson, Towson University, Mathematics Department
Dynamics
is the study of motion through phase space. The phase space of a given
dynamical system is described as an N-dimensional manifold, M. The topics
covered in this pdf are: Reference Materials, Dynamical Systems,
Bifurcations, Two-Dimensional Phase Flows, Nonlinear Oscillators,
Hamiltonian Mechanics, Maps, Strange Attractors, and Chaos, Ergodicity and
the Approach to Equilibrium, Front Propagation, Pattern Formation, Solitons,
Shock Waves.
Author(s): Daniel
Arovas, Department of Physics, University of California, San Diego
This set of
lecture notes is an attempt to convey the excitement of classical dynamics from
a contemporary point of view. Topics covered includes: Dynamical Systems,
Newtonian System, Variational Principle and Lagrange equations, The Hamiltonian
Formulation, Hamilton-Jacobi Theory, Non-linear Maps and Chaos.
This note covers
the following topics: Circle Diffeomorphisms, The Combinatorics of Endomorphisms,
Structural Stability and Hyperbolicity, Structure of Smooth Maps, Ergodic
Properties and Invariant Measures, Renormalization.
Author(s): Welington de Melo and Sebastian van Strien
This note
provides a broad introduction to Newtonian dynamics of particles and rigid
bodies with applications to engineering design. Topics covered includes:
kinematics and dynamics of particles and rigid bodies, conservation laws,
vibrations of single degree of freedom systems, and use of MATLAB to solve
equations of motion and optimize engineering designs.
This note the explains the following
topics: Newton’s Laws of Motion, One-Dimensional Motion, Multi-Dimensional
Motion, Planetary Motion, Two-Body Dynamics, Rotating Reference Frames, Rigid
Body Rotation, Lagrangian Dynamics, Hamiltonian Dynamics, Coupled
Oscillations, Gravitational Potential Theory, Lunar Motion and The
Chaotic Pendulum.
This course reviews
momentum and energy principles, and then covers the following topics:
Hamilton's principle and Lagrange's equations; three-dimensional kinematics
and dynamics of rigid bodies, steady motions and small deviations therefrom,
gyroscopic effects, and causes of instability, free and forced vibrations of
lumped-parameter and continuous systems; nonlinear oscillations and the phase
plane, nonholonomic systems, and an introduction to wave propagation in
continuous systems.
This is an introductory course on Newtonian mechanics and special
relativity given to first year undergraduates. The notes were last updated
in April 2012. Individual chapters and problem sheets are available on the
link below. The full set of lecture notes come in around 145 pages and can
be downloaded here. This covers the following topics: Newtonian Mechanics,
Forces, Interlude, Dimensional Analysis, Systems of Particles, Central
Forces, Rigid Bodies, Non-Inertial Frames and Special Relativity.The lecture
notes can be downloaded in both PDF and PS formats