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Notes 10: Renormalization (II)-Renormalization Representatives | Zhenghe's Blog
https://zhenghezhang.wordpress.com/2011/03/27/renormalization-ii
March 27, 2011. Notes 10: Renormalization (II)-Renormalization Representatives. Filed under: Schrodinger Cocycles. 8212; Zhenghe @ 6:01 pm. Recall in the last post we define. Then given a SL(2,R) cocycle dynamics. Is equivalent to a. We’ve also defined the renormalization operator. Is rescaling operator and. Is the basing change operator. By definition we have. In this post we will first analytically normalize. Because then the correponding. We state the normalizing result in the following Lemma. This ob...
Notes 12: Distributions of Eigenvalues of Ergodic 1D discrete Schrodinger operators in a.c. spectrum region | Zhenghe's Blog
https://zhenghezhang.wordpress.com/2011/05/18/notes-12-distribution-of-eigenvalues
May 18, 2011. Notes 12: Distributions of Eigenvalues of Ergodic 1D discrete Schrodinger operators in a.c. spectrum region. Filed under: Schrodinger Cocycles. 8212; Zhenghe @ 11:45 pm. Tags: Distribution of Eigenvalues. This post will be something about the distribution of eigenvalues of one dimensional discrete Schrodinger operators in absolutely continuous spectrum region. Namely, given a triple. And a potential function. Then these together generates a family of operators. Which is given by. Is some do...
Notes 11: Renormalization (III)-Convergence of Renormalization | Zhenghe's Blog
https://zhenghezhang.wordpress.com/2011/04/04/notes11-renormalization-iii-convergence-of-renormalization
April 4, 2011. Notes 11: Renormalization (III)-Convergence of Renormalization. Filed under: Dynamical Systems. 8212; Zhenghe @ 6:28 pm. Tags: Maximal Ergodic Theorem. I’ve been back to Evanston from Toronto. But I guess I still have 10 more notes to post. It will take me a very long time to finish. In this post we will discuss the convergence of renormalization. As pointed out in last post, it’s necessary that we should assume zero Lyapunov to get convergence. In fact, we will assume. We have for every.
Notes 9: Averaging and Renormalization(I)-Defining the Renormalization Operator | Zhenghe's Blog
https://zhenghezhang.wordpress.com/2011/03/03/notes-9-averaging-and-renormalization
March 3, 2011. Notes 9: Averaging and Renormalization(I)-Defining the Renormalization Operator. Filed under: Schrodinger Cocycles. 8212; Zhenghe @ 8:32 pm. This is post will be a breif introduction about some averaging and renormalization procedures in Schrodinger cocycles. Renormalization is everywhere in dynamical systems and it has been used by many people. Has already used them to construct counter-examples to Kotani-Last Conjecture. Be very Louville number. For instance, let. Grows sufficiently fast...
Notes 8:Examples(II)-Limit Periodic Potentials and Almost Mathieu Operator | Zhenghe's Blog
https://zhenghezhang.wordpress.com/2011/02/24/notes-8examplesii-limit-periodic-potentials-and-almost-mathieu-operator
February 24, 2011. Notes 8:Examples(II)-Limit Periodic Potentials and Almost Mathieu Operator. Filed under: Schrodinger Cocycles. 8212; Zhenghe @ 6:54 pm. Tags: almost mathieu operator. Example 3: Limit periodic potentials. There are two different equivalent ways to define limit periodic potentials. The first is that consider the. Is a compact Cantor group,. Is a minimal translation and. Is Haar measure. Let. Be continuous. Then this potential. It’s limit periodic if it can be approximated in. Can be any...
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A Chinese new year greeting~ | Area 777
https://conan777.wordpress.com/2012/01/23/a-chinese-new-year-greeting
Chasing dreams from mathematics to the real world. Carlos Matheus' blog. Guangbo Xu's blog. Ken Baker's blog. M@ Kahle's blog. Terry Tao's blog. Last page of sketchbook…. Year of 2015 – life in the strange world of consulting. Recent progress on the Imagineering quest. A posthumous paper: Random Methods in 3-manifolds. Progress update: Painting, drawing etc. 11/25/2013. Mathematics, with Imagination – a course proposal. Progress in painting: 08/172013-09/17/2013. A train track on twice punctured torus.
Dynamics of the Weil-Petersson flow: basic geometry of the Weil-Petersson metric II | Weblog
https://pfzhang.wordpress.com/2015/07/02/dynamics-of-the-weil-petersson-flow-basic-geometry-of-the-weil-petersson-metric-ii
Discussions (mainly my notes) related to Dynamics. Dynamics of the Weil-Petersson flow: basic geometry of the Weil-Petersson metric II. In the first post. Of this series, we planned to discuss in the third and fourth posts the proof of the following ergodicity criterion for geodesic flows in incomplete negatively curved manifolds of Burns-Masur-Wilkinson:. I) the universal cover $latex {M}&fg=000000$ of $latex {N}&fg=000000$ is geodesically convex. 7,622 more words. July 2, 2015 at 5:12 am. Leave a Reply...
Dynamics of the Weil-Petersson flow: basic geometry of the Weil-Petersson metric I | Weblog
https://pfzhang.wordpress.com/2015/07/02/dynamics-of-the-weil-petersson-flow-basic-geometry-of-the-weil-petersson-metric-i
Discussions (mainly my notes) related to Dynamics. Dynamics of the Weil-Petersson flow: basic geometry of the Weil-Petersson metric I. Today we will define the Weil-Petersson (WP) metric on the cotangent bundle of the moduli spaces of curves and, after that, we will see that the WP metric satisfies the first three items of the. Of Burns-Masur-Wilkinson (stated as Theorem 3 in the previous post. 7,184 more words. July 2, 2015 at 5:11 am. Under Uncategorized. No Comments. Or leave a trackback: Trackback URL.
Perron–Frobenius theorem | Weblog
https://pfzhang.wordpress.com/2015/05/23/perron-frobenius-theorem
Discussions (mainly my notes) related to Dynamics. Today I attended a lecture given by Vaughn Climenhaga. He presented a proof of the following version of Perron–Frobenius theorem:. Be the set of probability vectors,. Be a stochastic matrix with positive entries. Then. 8211;there is a positive probability. Therefore there exists some point. 2) Suppose on the contrary that there exists. That is also fixed by. Fixes every vector in the plane. In particular the points on. 3) We use the norm. Dynamics of the...
Some notes | Weblog
https://pfzhang.wordpress.com/2015/04/18/some-notes-2
Discussions (mainly my notes) related to Dynamics. Be a complete manifold,. Be the set of compact/closed subsets of $M$. Let. Be a complete metric space. Is said to be upper-semicontinuous at. For any open neighbourhood. There exists a neighbourhood. Viewed as a multivalued function, let. Be the graph of. Is usc. if and only if. Is a closed graph. Is said to be lower-semicontinuous at. For any open set. Or equally, for any. Be the set of. Note that it suffices to consider those points. The real decay rate.
Regularity of center manifold | Weblog
https://pfzhang.wordpress.com/2014/12/10/regularity-of-center-manifold
Discussions (mainly my notes) related to Dynamics. Regularity of center manifold. Is a fixed point of the generated flow on. Be the splitting into stable, center and unstable directions. Moreover, there are three invariant manifolds (at least locally) passing through. And tangent to the corresponding subspaces at. Theorem (Pliss). For any. Generally speaking, the size of the center manifold given above depends on the pre-fixed regularity requirement. Theoretically, there may not be a. Is tangent to plane.
Admissible perturbations of the tangent map | Weblog
https://pfzhang.wordpress.com/2015/02/06/admissible-perturbations-of-the-tangent-map
Discussions (mainly my notes) related to Dynamics. Admissible perturbations of the tangent map. Franks’s Lemma is a major tool in the study of differentiable dynamical systems. It says that along a simple orbit segment. Can be realized via a perturbation of the map. Which preserves the orbit segment). Moreover, such a perturbation is localized in a neighborhood of. And it can be made arbitrarily. Be a strictly convex domain,. Be the orbit along the/a diameter of. Is 2-period. Let. Is actually realizable ...
Progress in painting: 08/172013-09/17/2013 | Area 777
https://conan777.wordpress.com/2013/09/17/progress-in-painting-08172013-09172013
Chasing dreams from mathematics to the real world. Carlos Matheus' blog. Guangbo Xu's blog. Ken Baker's blog. M@ Kahle's blog. Terry Tao's blog. Last page of sketchbook…. Year of 2015 – life in the strange world of consulting. Recent progress on the Imagineering quest. A posthumous paper: Random Methods in 3-manifolds. Progress update: Painting, drawing etc. 11/25/2013. Mathematics, with Imagination – a course proposal. Progress in painting: 08/172013-09/17/2013. A train track on twice punctured torus.
Mathematics, with Imagination – a course proposal | Area 777
https://conan777.wordpress.com/2013/11/06/mathematics-with-imagination-a-course-proposal
Chasing dreams from mathematics to the real world. Carlos Matheus' blog. Guangbo Xu's blog. Ken Baker's blog. M@ Kahle's blog. Terry Tao's blog. Last page of sketchbook…. Year of 2015 – life in the strange world of consulting. Recent progress on the Imagineering quest. A posthumous paper: Random Methods in 3-manifolds. Progress update: Painting, drawing etc. 11/25/2013. Mathematics, with Imagination – a course proposal. Progress in painting: 08/172013-09/17/2013. A train track on twice punctured torus.
Back to the drawing board — Month #1 (and a bit more) | Area 777
https://conan777.wordpress.com/2013/07/17/back-to-the-drawing-board-month-1-and-a-bit-more
Chasing dreams from mathematics to the real world. Carlos Matheus' blog. Guangbo Xu's blog. Ken Baker's blog. M@ Kahle's blog. Terry Tao's blog. Last page of sketchbook…. Year of 2015 – life in the strange world of consulting. Recent progress on the Imagineering quest. A posthumous paper: Random Methods in 3-manifolds. Progress update: Painting, drawing etc. 11/25/2013. Mathematics, with Imagination – a course proposal. Progress in painting: 08/172013-09/17/2013. A train track on twice punctured torus.
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Zhenghe's Blog | Math blog
May 18, 2011. Notes 12: Distributions of Eigenvalues of Ergodic 1D discrete Schrodinger operators in a.c. spectrum region. Filed under: Schrodinger Cocycles. 8212; Zhenghe @ 11:45 pm. Tags: Distribution of Eigenvalues. This post will be something about the distribution of eigenvalues of one dimensional discrete Schrodinger operators in absolutely continuous spectrum region. Namely, given a triple. And a potential function. Then these together generates a family of operators. Which is given by. Is some do...
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