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000839251 019__ $$a1036104374$$a1037008333$$a1040651620
000839251 020__ $$a9783319776613$$q(electronic book)
000839251 020__ $$a3319776614$$q(electronic book)
000839251 020__ $$z9783319776606
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000839251 0247_ $$a10.1007/978-3-319-77661-3$$2doi
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000839251 1001_ $$aBaladi, Viviane,$$eauthor.
000839251 24510 $$aDynamical Zeta functions and dynamical determinants for hyperbolic maps :$$ba functional approach /$$cViviane Baladi.
000839251 264_1 $$aCham, Switzerland :$$bSpringer,$$c2018.
000839251 300__ $$a1 online resource (xv, 291 pages) :$$billustration.
000839251 336__ $$atext$$btxt$$2rdacontent
000839251 337__ $$acomputer$$bc$$2rdamedia
000839251 338__ $$aonline resource$$bcr$$2rdacarrier
000839251 347__ $$atext file$$bPDF$$2rda
000839251 4901_ $$aErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,$$x0071-1136 ;$$vvolume 68
000839251 504__ $$aIncludes bibliographical references and index.
000839251 5050_ $$aIntro; Preface; Contents; Index of notations; 1 Introduction; 1.1 Statistical properties of chaotic differentiable dynamical systems; 1.2 Transfer operators. Dynamical determinants. Resonances; 1.3 Main results. Examples; 1.4 Main techniques; Comments; Part I Smooth expanding maps; 2 Smooth expanding maps: The spectrum of the transfer operator; 2.1 Transfer operators for smooth expanding maps on Hölder functions; 2.2 Transfer operators for smooth expanding maps on Sobolev spaces; 2.2.1 Isotropic Sobolev spaces Htp and good systems of charts
000839251 5058_ $$a2.2.2 Bounding the essential spectral radius (Theorem 2.15)2.2.3 The key local Lasota-Yorke bound (Lemma 2.21); 2.2.4 Fragmentation and reconstitution: Technical lemmas; 2.3 The essential spectral radius on Sobolev spaces: Interpolation; 2.3.1 Complex interpolation; 2.3.2 Proof of Theorem 2.15 on Htp for integer differentiability; 2.4 The essential spectral radius: Dyadic decomposition; 2.4.1 A Paley-Littlewood description of Htp and Ct*; 2.4.2 Proof of Lemma 2.21 and Theorem 2.15: The general case; 2.5 Spectral stability and linear response à la Gouëzel-Keller-Liverani; Problems; Comments
000839251 5058_ $$a3 Smooth expanding maps: Dynamical determinants3.1 Ruelle's theorem on the dynamical determinant; 3.1.1 Dynamical zeta functions; 3.2 Ruelle's theorem via kneading determinants; 3.2.1 Outline; 3.2.2 Flat traces; 3.3 Dynamical determinants: Completing the proof of Theorem 3.5; 3.3.1 Proof of Theorem 3.5 if >d+t; 3.3.2 Nuclear power decomposition via approximation numbers; 3.3.3 Asymptotic vanishing of flat traces of the non-compact term; 3.3.4 The case d+t of low differentiability; Problems; Comments; Part II Smooth hyperbolic maps; 4 Anisotropic Banach spaces defined via cones
000839251 5058_ $$a4.1 Transfer operators for hyperbolic dynamics4.1.1 Hyperbolic dynamics and anisotropic spaces; 4.1.2 Bounding the essential spectral radius (Theorem 4.6); 4.1.3 Reducing to the transitive case; 4.2 The spaces Wp,*t,s and Wp,**t,s; 4.2.1 Charts and cone systems adapted to (T,V); 4.2.2 Formal definition of the spaces Wp,*t,s and Wp,**t,s; 4.3 The local Lasota-Yorke lemma and the proof of Theorem 4.6; 4.3.1 The Paley-Littlewood description of the spaces and the local Lasota-Yorke lemma; 4.3.2 Fragmentation, reconstitution, and the proof of Theorem 4.6; Problems; Comments
000839251 5058_ $$a5 A variational formula for the essential spectral radius5.1 Yet another anisotropic Banach space: Bt,s; 5.1.1 Defining Bt,s; 5.2 Bounding the essential spectral radius on Bt,s (Theorem 5.1); 5.3 Spectral stability and linear response; Problems; Comments; 6 Dynamical determinants for smooth hyperbolic dynamics; 6.1 Dynamical determinants via regularised determinants and flat traces; 6.2 Proof of Theorem 6.2 on dT,g(z) if r-1> d+ t-s; 6.3 Theorem 6.2 in low differentiability r-1d+t-s; 6.4 Operators on vector bundles and dynamical zeta functions; Problems; Comments
000839251 506__ $$aAccess limited to authorized users.
000839251 520__ $$aThe spectra of transfer operators associated to dynamical systems, when acting on suitable Banach spaces, contain key information about the ergodic properties of the systems. Focusing on expanding and hyperbolic maps, this book gives a self-contained account on the relation between zeroes of dynamical determinants, poles of dynamical zeta functions, and the discrete spectra of the transfer operators. In the hyperbolic case, the first key step consists in constructing a suitable Banach space of anisotropic distributions. The first part of the book is devoted to the easier case of expanding endomorphisms, showing how the (isotropic) function spaces relevant there can be studied via Paley–Littlewood decompositions, and allowing easier access to the construction of the anisotropic spaces which is performed in the second part. This is the first book describing the use of anisotropic spaces in dynamics. Aimed at researchers and graduate students, it presents results and techniques developed since the beginning of the twenty-first century.
000839251 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed May 15, 2018).
000839251 650_0 $$aFunctions, Zeta.
000839251 650_0 $$aDynamics.
000839251 650_0 $$aBanach spaces.
000839251 650_0 $$aGeometry, Hyperbolic.
000839251 77608 $$iPrint version: $$z3319776606$$z9783319776606$$w(OCoLC)1022789852
000839251 830_0 $$aErgebnisse der Mathematik und ihrer Grenzgebiete ;$$v3. Folge, Bd. 68.
000839251 852__ $$bebk
000839251 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-77661-3$$zOnline Access$$91397441.1
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