%PDF-1.4 % 4 0 obj << /S /GoTo /D (43section.1) >> endobj 7 0 obj (1. Introduction) endobj 8 0 obj << /S /GoTo /D (43section.8) >> endobj 11 0 obj (2. Simple cylinder invariant under the involution) endobj 12 0 obj << /S /GoTo /D (43subsection.9) >> endobj 15 0 obj (2.1. Translation surfaces of genus one) endobj 16 0 obj << /S /GoTo /D (43subsection.10) >> endobj 19 0 obj (2.2. Saddle connection preserved by the involution) endobj 20 0 obj << /S /GoTo /D (43section.15) >> endobj 23 0 obj (3. Proof of Theorem 1.1) endobj 24 0 obj << /S /GoTo /D (43subsection.16) >> endobj 27 0 obj (3.1. Existence of simple cylinder on hyperelliptic translation surfaces) endobj 28 0 obj << /S /GoTo /D (43subsection.20) >> endobj 31 0 obj (3.2. Proof of Theorem 1.1) endobj 32 0 obj << /S /GoTo /D (43section.22) >> endobj 35 0 obj (4. Splitting of surfaces in H\032hyp\(4\)) endobj 36 0 obj << /S /GoTo /D (43subsection.23) >> endobj 39 0 obj (4.1. Flat torus with a marked geodesic segment) endobj 40 0 obj << /S /GoTo /D (43subsection.25) >> endobj 43 0 obj (4.2. The space of splittings) endobj 44 0 obj << /S /GoTo /D (43subsection.32) >> endobj 47 0 obj (4.3. Special splitting) endobj 48 0 obj << /S /GoTo /D (43subsection.34) >> endobj 51 0 obj (4.4. Ratner's Theorem) endobj 52 0 obj << /S /GoTo /D (43section.39) >> endobj 55 0 obj (5. Surfaces admitting special splitting are contained in the orbit closure) endobj 56 0 obj << /S /GoTo /D (43subsection.41) >> endobj 59 0 obj (5.1. Dual splitting) endobj 60 0 obj << /S /GoTo /D (43subsection.44) >> endobj 63 0 obj (5.2. Changing splitting) endobj 64 0 obj << /S /GoTo /D (43subsection.65) >> endobj 67 0 obj (5.3. Proof of Proposition 5.1) endobj 68 0 obj << /S /GoTo /D (43section.66) >> endobj 71 0 obj (6. Proof of Theorem 4.3) endobj 72 0 obj << /S /GoTo /D (43section.68) >> endobj 75 0 obj (7. Proof of Theorem 1.2) endobj 76 0 obj << /S /GoTo /D (43section.74) >> endobj 79 0 obj (8. Surfaces admitting completely periodic directions with three cylinders) endobj 80 0 obj << /S /GoTo /D (43subsection.75) >> endobj 83 0 obj (8.1. Two models of decomposition into three cylinders) endobj 84 0 obj << /S /GoTo /D (43subsection.79) >> endobj 87 0 obj (8.2. Proof of Corollary 1.3) endobj 88 0 obj << /S /GoTo /D (43subsubsection.80) >> endobj 91 0 obj (8.2.1. Proof of Corollary 1.3, Case \(I\)) endobj 92 0 obj << /S /GoTo /D (43subsubsection.81) >> endobj 95 0 obj (8.2.2. Proof of Corollary 1.3, Case \(II\)) endobj 96 0 obj << /S /GoTo /D (43section.83) >> endobj 99 0 obj (9. Applications) endobj 100 0 obj << /S /GoTo /D (43subsection.84) >> endobj 103 0 obj (9.1. Generic surfaces with coordinates in a quadratic field) endobj 104 0 obj << /S /GoTo /D (43subsection.86) >> endobj 107 0 obj (9.2. Thurston\205Veech surface with cubic trace field) endobj 108 0 obj << /S /GoTo /D (43section*.100) >> endobj 111 0 obj (References) endobj 112 0 obj << /S /GoTo /D [113 0 R /FitBH ] >> endobj 121 0 obj << /Length 3499 /Filter /FlateDecode >> stream x[[۶~P^:Ԍ"Lssqni