Lecture Notes on Dynamical Systems, Chaos And Fractal Geometry
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
This note describes the following topics: Equation of motion, Equations of motion for an inviscid fluid,
Bernoulli equation, The vorticity field, Two dimensional flow of a homogeneous,
incompressible, inviscid fluid and boundary layers in nonrotating fluids.
Topics covered in the
notes include : Introduction and Newton’s Laws , Kinematics, Forces, Energy,
Motion near equilibrium, Damped vibrations, Conservation of momentum,
Angular momentum and central forces, Waves on a string.
The contents of this pdf include : Introduction
to Mechanical Vibrations, Vibration Under Harmonic Forcing Conditions,
Vibration Under General Forcing Conditions, Two and Multi - Dof System,
Continuous Systems.
Author(s): G S D Madhav,
Assistant Professor, Y Shwetha, Assistant Professor, G Ram Vishal,
Assistant Professor, Department of Aeronautical Engineering, Institute
of Aeronautical Engineering
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
This note explains the following topics: Introduction to the
dynamics and vibrations of lumped-parameter models of mechanical systems,
Work-energy concepts, Kinematics, Force-momentum formulation for systems of
particles and rigid bodies in planar motion, Lagrange's
equations for systems of particles and rigid bodies in planar motion,
Virtual displacements and virtual work, Linearization of equations of
motion, Linear stability analysis of mechanical systems.
Author(s): Prof. Nicholas Hadjiconstantinou, Prof. Peter So, Prof. Sanjay Sarma and Prof.
Thomas Peacock
This note covers the
following topics: Kinematics of Particles, Rectilinear, Curvilinear x-y,
Normal-tangential n-t, Polar r-theta, Relative motion, Force Mass Acceleration,
Work Energy, Impulse Momentum, Kinematics of Rigid Bodies, Rotation, Absolute
Motion, Relative Velocity, Relative Acceleration, Motion Relative to Rotating
Axes, Force Mass Acceleration and Kinetics of Rigid Bodies.