Chaos Definition and 188 Threads

When looking for chaos in the n body problem what should i do?

Homework Statement Identify the stable, unstable and center eigenspaces for \dot{y} = the 3x3 matrix row 1: 0, -3, 0 row 2: 3, 0, 0 row 3: 0, 0, 1 Homework Equations The Attempt at a Solution This is an example used from the lecture and I understand how to get the...

Basically where are nonlinear dynamics and chaos theory used in the real world? Like if someone studies it what type of areas might they find it being useful for? The only example I can seem to think of is stuff like weather/fluids/air resistance/physics. What might be some other more...

http://www.technologyreview.com/blog/arxiv/27628/?p1=blogs For those who might not know of the theory the goal of quantum chaos theory is to explain all of classical physics including classical chaos as emerging from quantum systems. They've had some experimental success in the past, but this...

Hey guys, I am thinking about world at small scale and world at larger scale. Why world is more chaos at smaller scale and why it is more smooth and uniform in larger scale?

Is there any parameter that represents the chaotic-ness of a system? For example, can we show that a 4-body system is in general more chaotic than a 3-body problem? Thank you : )

As the thread title says I'm interested in Chaos Theory, Complex Systems, and Nonlinear Systems. If I can help it, I'd like to study these at graduate level. My question is what kind and how much mathematics I'm supposed to know if I'm to study these?

I have to conduct a physics research report on Chaos Theory. From background reading i understand it to be a very maths based topic so my question is how do i relate chaos theory to physics? What sort of sub topics should i be researching? Any responses greatly appreciated!

Usually positive Ljapunov exponent is said to be a condition for chaos, and the strange atractor is so. Are there any theorem which shows that the two condition is equivalent? They are necessary and sufficent conditions?

I've been doing a lot of reading on chaos lately. Things like the butterfly effect, the logistic equation, the Lorenz attractor, etc. It's all great and wonderful but I'm finding things very un-unified. I understand that certain nonlinear systems can sometimes exhibit chaotic behavior, but...

Dear Physics Forum community. Please allow me tro preface the following by stating that I am a novice to the concept of chaos theory. Although I do understand the general concept behind Turing, Bellousov, Laurenz and Madelbrot's concepts, I am not entirely familiar with the mathematical basis...

Apologies for the confusingly worded title; i was trying to keep it short. If the universe reaches a state of maximum entropy (as in the Heat Death theory), why would that state be stable. Wouldnt entropy be infinite and therefore any state, including the maximumly ordered state of the Big...

The word 'cosmos' is defined as an orderly harmonious systematic universe. There are some people who actually think that disorder, randomness and chaos is a better description of the Universe, but I disagree. For the most part the Universe exhibits a very high degree of order, harmony and...

In the following video Penrose states that the Universe was so special and organized at its initial state the figure describing it would be "at least" 10^123. Begin at 4:50 Has this figure or any other figure been confirmed? Where can I go to find out if this is true or not. I found...

Of course, the second law of thermodynamics implies that all closed systems will go from a state of state of order to disorder. Chaos theory offers the possibility of systems developing patterns and order from seemingly disordered or chaotic systems. Do these theories contradict or is there...

If you haven't watched it, can be found here: I watched the second time today and it was absolutely astonishing, didn't quite "get it" the first time. It pretty much explains how life originates. I don't think anything can be added to what the program wanted to convey. I would like to...

I am agile with Science but my Career was Chaotic except now 2010 [FONT="Arial Black"][SIZE="3"] I am passionate about Science but my Career was always in downturn except now 2010 i am Curious to become a Scientist r a researcher but i am already 25years old n everyone tells me that i am...

I really like fractals and what I find even more amazing, is that something so beautiful can be so useful. I've heard that they can be used for example in chaos. I've gone through about 10 websites and all were about fractals and chaos. But I couldn't find a single sentence that would tell me...

MTd2 spotted this interesting paper by Florian Conrady (Perimeter postdoc). To go with this paper the author has provided two animations to watch: http://www.florianconrady.com/simulations.html The second one of these two simulations ("Model with 2D interactions") shows the crystalization of...

Hello, I've used the search button but the topic I found on it didn't quite answer my questions, so here is my go at it: (I have done one year of maths at college, to know my level in case it's important for formulating your answer) So I've started reading "The End of Certainty" by Prigogine...

what is quantum chaos? dose it exist realy? the original definition of classical chaos is a system with exponential sensitivity to initial conditions. however in quantum mechanics because of the linear property of the schrodinger equation, variation on initial condition of the wave function...

So I've recently been reading up a bit on Chaos theory. It seems like a pretty cool idea (that's all I can say about it, because I don't have a true, full understanding of it) but my question is this: Is it still being studied? I'm reading CHAOS by James Gleick(basically the definition of...

Hi I'm new to this and sorry if this is not the correct place to post this. I was wondering if people still study chaos theory? (sorry if its a silly question) And if they do where chaos scientists work and what are the main things you need to study so you can study chaos theory. Thank you

I have a BS in math and to think of it Chaos theory was why I got into this field to begin with. Which educational/career path should i follow from now on?

Does the following statement make sense: The Chaos theory models systems (e.g., gases, fluids, sound, populations, whether, solar system) which particles (e.g., atoms, waves, specimens, currents, planets) shift from entropy to harmony following certain laws (e.g, thermodynamic, mass, space...

Microwave defrost :"Chaos" ? The defrost cycle on my microwave oven claims to use "Chaos". Can this be a serious Engineering idea or is it just a flahsy sounding term, meaning nothing?

Hi there, My objective is to study Hamiltonian systems, integrable and non integrable systems, where there will be chaos, etc. I have a general idea of everything.. the destroyed tori, the symplectic structure of hamilton's equations, etc. But nothing is very clear to me! And the most...

I have studied fractals and think of them as things that exhibit self similarity at different characteristic scales. For example a grain of sand looks a bit like a pebble, which looks a bit like an outcrop, which looks a bit like a mountain. If you count the number of grains of sand there will...

i am now reading a prl paper the authors used numerical simulations to study a nonlinear system in some parameters, the authors state that system enters into chaos My numerical simulations are the same as that of the authors in the regular regime but in the chaos regime, my...

i am now reading a prl paper the authors used numerical simulations to study a nonlinear system in some parameters, the authors state that system enters into chaos My numerical simulations are the same as that of the authors but in the chaos regime, my simulations are quite different...

Is there a line between a system in chaos and one not in chaos? Alternatively, is there a transition zone? If such things do exits, what are they called?

i apologize if my terminology is not correct because I am kind of new to this theology stuff. I know there is a theory, I'm not sure if it's chaos theory, that states that all things move toward disorganization or chaos rather than organization. This seems to be true in the broad sense of...

Are there any attempts to synthesize between these two theories? I mean are there methods from QFT being used in QC and vice versa? I asked one professor from my univ if I were to research under his belt in QC, would I need some QFT knowledge and he said not. So I wonder are they really...

Hi! I'm perusing fractals out of personal interest. Although I come from physics, I have a background in math-major undergrad mathematics (complex analysis, a bit of modern algebra). I find Mandelbrot's Fractal Geometry of Nature relatively light reading, but I am interested in a more standard...

Hi, I've read a little bit about fractals, being self repeating shapes. Is there a connections between fractals and chaotic systems? Thanks

Hello ! I'm looking for a paper or a link that would report observational evidence of chaos behaviour for the three-body problem. Thanks for helping me.

Homework Statement Consider the families of iterating functions Fλ(x) = λ(x3 - x). Fλ(x) undergoes a bifurcation at λ=1, about the fixed point x=0. Figure out what ilk of bifurcation is occurring for Fλ(x) and prove your assertion rigorously.Homework Equations My book says this about...

There has been much controversy concerning Global Warming: sun spot activity, only heat radiation at 15 microns being trapped by CO2, vast amounts of greenhouse gases going intot he atmosphere from exploding volcanos and the general cyclical nature of climate change have attempted to explain the...

Hello there I have to write an interdisciplinary project at school, in mathematics and physics, where I have to go beyond what is covered in the syllabus for mathematics. I have chosen the subject of chaos theory. Can you recommend any good introductions, on this subject? And would I need...

I can't believe it...there has just been a traffic circle built in my neighborhood. How exotic! It's just around the corner from me - the SQUARE corner. The center of the circle is still just dirt. So far I have seen two cars dirve straight across it! Someone's going to get killed out...

the decrease of the information v.s. chaos ?? One book about Chaos says that we can use the decrease of the information of the system to define whether the system is chaotic or not. I don't know why and how to do it? If you know about it, can you show it to me, or you can tell me the...

can someone give me some hints on studying chaos theory? like some introductory websites, good introductory texts, prerequisites for studying? edit how readable is "The Fractal Geometry of Nature" by mandlebrot?

I will talk about the quantum chaos. Quantum chaos comes from the classical chaos. unfortunately, the concept of trajectory is forbidden in quantum theory. So it is very difficult to define the quantum chaos. Now many works use lots of methods to define it, for example, Random-Matrix theory...

Hi! i just wanted to know if the famous Chaos Theory has got any direct application in Aeronautics. i've come across some information regarding this. the theory finds quite a bit of use in the study of turbulence, but then I'm unable to find some good reference material to get more relevant...

Homework Statement The center of a circular billiard is harmonically oscillating in horizontal direction with the amplitude a and frequency omega. Describe the motion of elastic particle with mass m in this billiard. Use the proper phase space and Poincare map. Under what conditions...

Does anyone have a recommendation on an introductory chaos theory text? I would like a text that is either upper division undergrad, or possibly at the graduate level. Also, are there any "classics" or bibles in the field? Thanks you,

I am thinking of taking this as an elective next year (mainly because it sounds cool and I need math credits), but I have no idea of what to expect. Anyone taken a similar course before? What kind of material is covered? Is it interesting/useful?

What is the difference between nonlinearity and chaos, or is there a difference?

I recently heard that there are two main phenomenons which are discussed in statistics: chaos and randomness. What exactly is the difference between the two?

Hi, The following problem is from Halliday and Resnick's Physics, Vol. I, 1967 edition, page 379, Problem 35. It has defeated me for the last month. "A particle undergoes motion in the x-y plane. It's equation of motion is given by x = A_x cos(w_x t) y = A_y cos(w_y t) (i)If the...